![Ontology as a Logic of Intensions
Marie DUŽÍa,1
, Martina ÍHALOVÁa
, Marek MENŠÍKa,b
a
VSB-Technical University Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic
b
Institute of Computer Science, FPF, Silesian University in Opava, Bezruovo nám. 13,
746 01 Opava, Czech Republic
m.tina.cihal@gmail.com, marie.duzi@vsb.cz, mensikm@gmail.com
Abstract. We view the content of ontology via a logic of intensions. This is due to
the fact that particular intensions like properties, roles, attributes and propositions
can stand in mutual necessary relations which should be registered in the ontology
of a given domain, unlike some contingent facts. The latter are a subject of updates
and are stored in a knowledge-base state. Thus we examine (higher-order)
properties of intensions like being necessarily reflexive, irreflexive, symmetric,
anti-symmetric, transitive, etc., mutual relations between intensions like being
incompatible, being a requisite, being complementary, and so like. We also define
two kinds of entailment relation between propositions, viz. mere entailment and
presupposition. Finally, we show that higher-order properties of propositions
trigger necessary integrity constraints that should also be included in the ontology.
As the logic of intensions we vote for Transparent Intensional Logic (TIL),
because TIL framework is smoothly applicable to all three kinds of context, viz.
extensional context of individuals, numbers and functions-in-extension (mappings),
intensional context of properties, roles, attributes and propositions, and finally
hyper-intensional context of procedures producing intensional and extensional
entities as their products.
Keywords. Ontology, intension, hyperintension, Transparent Intensional Logic,
integrity constraint.
Introduction
In informatics, the term ‘ontology’ has been borrowed from philosophy, where
ontology is a systematic account of existence. In most general, what exists is that what
can be represented. Thus in recent Artificial Intelligence and information systems a
formal ontology is an explicit and systematic conceptualization of a domain of interest.
Given a domain, ontological analysis should clarify the structure of knowledge on what
exists in the domain. A formal ontology is, or should be, a stable heart of an
information system that makes knowledge sharing, reuse and reasoning possible. As J.
Sowa says in [14, p. 51], “logic itself has no vocabulary for describing the things that
exist. Ontology fills that gap: it is the study of existence, of all the kinds of entities
abstract and concrete that make up the world”.
Current languages and tools applicable in the area of an ontology design focus in
particular on the form of ontological representation rather than what a semantic content
of ontology should be. Of course, a unified syntax is useful, but the problems of syntax
1
Corresponding Author.
Information Modelling and Knowledge Bases XXII
A. Heimbürger et al. (Eds.)
IOS Press, 2011
© 2011 The authors and IOS Press. All rights reserved.
doi:10.3233/978-1-60750-690-4-1
1](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-15-320.jpg)
![are almost trivial compared to the problems of developing a common semantics for any
domain. In this paper we focus on ontology content rather than a form. We concentrate
on describing concepts necessary for the specification of relations between higher-order
entities like properties, roles/offices, attributes and propositions, which are all modelled
as PWS (possible-world semantics) intensions, i.e. functions with the set of possible
worlds as their domain. To this end we apply the procedural semantics of Transparent
Intensional Logic (TIL), which provides a universal framework applicable smoothly in
all three kinds of context, namely extensional context of individuals, numbers and
functions-in-extension, intensional context of PWS-intensions and finally hyper-
intensional context of concepts viewed as abstract procedures producing extensional as
well as intensional entities as their products.2
The paper is organised as follows. Ontology content and languages for ontology
specification are introduced in Section 1. Here we also provide a brief introduction to
Transparent Intensional Logic, the tool we are going to apply throughout the paper. In
Section 2 we introduce our logic of intensions, in particular the logic of requisites.
Section 3 tackles the phenomenon of presupposition and compares it with mere
entailment. Finally, concluding Section 4 outlines further research.
1. Ontology content and knowledge representation
Knowledge representation is a multidisciplinary discipline that applies theories and
tools of logic and ontology. It comprises both knowledge base and ontology design.
Yet there is a substantial distinction between the former and the latter. Whereas the
content of a knowledge base state consists in particular of contingent values of
(empirical) attributes, the ontology content comprises in particular the taxonomy of
entities that should not depend on contingent facts. Thus, for instance in Description
Logic (DL) we distinguish between definitional and incidental part, the former
containing concepts of attributes rather than their values. The main reason for building
knowledge-based systems comprising ontologies can be characterized as making
hidden knowledge explicit and logically tractable. To this end it is desirable to apply an
expressive semantic framework in order that all the semantically salient features of
knowledge specification can be adequately represented so that reasoning based on this
representation is logically adequate and does not yield paradoxes.
In general, current ontology languages are mostly based on the 1st
-order predicate
logic (FOL). Though FOL has become stenography of mathematics, it is not expressive
enough when applied in other areas such as ontology specification. The obvious
shortcoming of the FOL approach is this: in FOL we must treat higher-order intensions
and hyper-intensions as elements of a flat universe, due to which knowledge
representation is not comprehensible enough. Moreover, when representing knowledge
in FOL, the well-known problem of the paradox of omniscience is almost inevitable.
For applications where FOL is not adequate, it would be desirable to extend the
framework to a higher-order logic (HOL). A general objection against using HOL logic
is its computational intractability. However, HOL formulas are relatively well
understood, and reasoning systems for HOLs do already exist, e.g., HOL [6] and
Isabel [13].
2
Recent most up-to-date results and applications of TIL can be found in [5].
M. Duží et al. / Ontology As a Logic of Intensions
2](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-16-320.jpg)
![1.1. Standard ontological languages
There are a number of languages which have been developed for knowledge
representation. They provide tools for knowledge-base specification and deductive
reasoning using the specified knowledge. Of these, perhaps the best known and broadly
used logical calculi are F-logic and Description Logic (DL) in their various variants.3
The F-logic arose from the practice of frame systems. Thus it can be viewed as a
hierarchy of classes of elements which are furnished with attributes, accompanied by
inference rules. The DL-philosophy is different; it makes use of the notion of a logical
theory defined as a set of special axioms built over the first-order predicate logic
calculus. Particular classes and their mutual relations are defined by logical formulas.
Thus in DL the class hierarchy typical for frame systems is not directly specified.
Rather, it is dynamically derived using logical definitions (class descriptions).
Though the existing ontology languages have been enriched by a few constructs
exceeding the power of FOL, these additional constructs are usually not well defined
and understood. Moreover, particular languages are neither syntactically nor
semantically compatible.
The W3C efforts at standardization resulted in accepting the Resource Description
Framework (RDF) language as the Web ontological recommendation. However, this
situation is far from satisfactory. Quoting from Horrocks and Schneider [8]: “The
thesis of representation underlying RDF and RDFS is particularly troublesome in this
regard, as it has several unusual aspects, both semantic and syntactic. A more-standard
thesis of representation would result in the ability to reuse existing results and tools in
the Semantic Web.” RDF includes three basic elements. Resources are anything with
an URI address. Properties specify attributes and/or (binary) relations between
resources and an object used to describe resources. Statements of the form ‘subject,
predicate, object’ associate a resource and a specific value of its property. RDF has
unusual aspects that make its use as the foundation of representation in the area of
ontology building and Semantic Web difficult at best. In particular, RDF has a very
limited collection of syntactic constructs, and these are treated in a very uniform
manner in the semantics of RDF. The RDF syntax consists of the so-called triples –
subject, predicate and object, where only binary predicates are allowed. This causes
serious problems concerning compatibility with more expressive languages. The RDF
thesis requires that no other syntactic constructs than the RDF triples are to be used and
that the uniform semantic treatment of syntactic constructs cannot be changed only
augmented. In RDFS we can specify classes and properties of individuals, constraints
on properties, and the relation of subsumption (subclass, subproperty). It is not possible,
for instance, to specify properties of properties, e.g., that the relation (property) is
functional or transitive. Neither it is possible to define classes by means of properties of
individuals that belong to the class. The RDF like languages originally did not have a
model theoretic semantics, which led to many discrepancies. As stated above, RDF(S)
is recommended by W3C, and its usage is world spread. The question is whether it is a
good decision. A classical FOL approach would be better, or even its standard
extension to HOL would be more suitable for ontologies. Formalisation in HOL is
much more natural and comprehensive, the universe of discourse is not a flat set of
‘individuals’; rather, properties and relations can be naturally talked about as well,
which is much more apt for representation of ontologies.
3
For details on Description Logic and F-logic see, for instance, [1] and [11], respectively.
M. Duží et al. / Ontology As a Logic of Intensions 3](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-17-320.jpg)
![Recognition of the limitations of RDFS led to the development of ontology
languages such as OIL, DAML-ONT and DAML+OIL, which resulted into the OWL.
OWL has been developed as an extension of RDFS. OWL (like DAML+OIL) uses the
same syntax as RDF (and RDFS) to represent ontologies, the two languages are
syntactically compatible. However, the semantic layering of the two languages is more
problematical. The difficulty stems from the fact that OWL (like DAML+OIL) is
largely based on DL, the semantics of which would normally be given by a classical
first-order model theory in which individuals are interpreted as elements of some
domain (a set), classes are interpreted as subsets of the domain and properties are
interpreted as binary relations on the domain. The semantics of RDFS, on the other
hand, are given by a non-standard model theory, where individuals, classes and
properties are all elements in the domain. Properties are further interpreted as having
extensions which are binary relations on the domain, and class extensions are only
implicitly defined by the extension of the rdf:type property. Moreover, RDFS supports
reflection on its own syntax: interpretation of classes and properties can be extended by
statements in the language. Thus language layering is much more complex, because
different layers subscribe to these two different approaches.
A bit more sophisticated approach is provided by the OWL (Ontology Web
Language) that is also recommended by W3C, which is based on DL framework. In
DL we talk about individuals that are elements of a universe domain. The individuals
are members of subclasses of the domain, and can be related to other individuals (or
data values) by means of properties (n-ary relations are called properties in Web
ontologies, for they are decomposed into n properties). The universe of discourse is
divided into two disjoint sorts: the object domain of individuals and the data value
domain of numbers. Thus the interpretation function assigns elements of the object
domain to individual constants, elements of data value domain to value constants, and
subclasses of the data domain to data types. Further, object and data predicates are
distinguished, the former being interpreted as a subset of the Cartesian product of
object domain, the latter a subset of the Cartesian product of value domain. DL is rather
rich, though being an FOL language. It makes it possible to distinguish intensional
knowledge (knowledge on the analytically necessary relations between concepts) and
extensional knowledge (of contingent facts). To this end DL knowledge base includes
the so-called T-boxes (terminology or taxonomy) and A-boxes (contingent attributes of
objects). T-box contains verbal definitions, i.e., a new concept is defined composing
known concepts. For instance, a woman can be defined: WOMAN = PERSON SEX-
FEMALE, and a mother: MOTHER = WOMAN child(HASchild). Thus the fact
that, e.g., mother is a woman is analytic (necessary) truth. In T-boxes there are also
specifications of necessary properties of concepts and relations between concepts: the
property satisfiability corresponds to a nonempty concept, the relation of subsumption
(intensionally contained concepts), equivalence and disjointness (incompatibility).
Thus, e.g., that a bachelor is not married is analytically true proposition. On the other
hand, the fact that, e.g., Mr. Jones is a bachelor is a contingent unnecessary fact. Such
contingent properties (attributes) of objects are recorded in A-boxes.
The third group of ontology languages lies somewhere between the FOL
framework and RDFS. This group comprises SKIF and Common Logic [7]. The SKIF
syntax is compatible with functional language LISP, but in principle it is an FOL
syntax. These languages also have a non standard model theory, with predicates being
interpreted as individuals, i.e., elements of a domain. Classes are however treated as
subsets of the domain, and their redefinition in the language syntax is not allowed.
M. Duží et al. / Ontology As a Logic of Intensions
4](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-18-320.jpg)
![Based on common logic, the SKIF language accommodates some higher-order
constructs. The SKIF languages are syntactically compatible with LISP, i.e., the FOL
syntax is extended with the possibility to mention properties and use variables ranging
over properties. For instance, we can specify that John and Peter have a common
property: p.p(John) p(Peter). The property they have in common can be, e.g., that
they both love their wives. We can also specify that a property P is true of John, and
the P has the property Q: P(John) Q(P). If P is being honest and Q is being eligible,
the sentence can be read as that John is honest, which is eligible. The interpretation
structure is a triple ¢D, ext, V², where D is the universe, V is the function that maps
predicates, variables and constants to the elements of D, and ext is the function that
maps D into sets of n-tuples of elements of D. SKIF does not reduce the arity of
predicates.
To our best knowledge, the only ontology language supporting inferences at this
level is a Semantic Web Rule Language (SWRL) combining OWL and RuleML [9].
According to the OWL (Web Ontology Language) overview [19], OWL is intended to
be used when information contained in documents needs to be processed by
applications, as opposed to situations where the contents only need to be presented to
humans. OWL can be used to represent the meaning of terms in vocabularies and
relationships between those terms. OWL has been designed on the top of XML, XLink,
RDF and RDFS in order to provide more facilities for expressing meaning and
semantics to represent machine interpretable content on the Web.
Summarising, well-defined ontology should serve at least these goals:
(1) universal library to be accessed and used by humans in a variety of information use
contexts,
(2) the backdrop work of computational agents carrying out activities on behalf of
humans, and
(3) a method for integrating knowledge bases and databases to perform tasks for
humans.
Current ontology languages, however, are far from meeting these goals, and their
expressive power does not enable computational agents to make use of an adequate
inference machine. Still worse, from a logical-semantic point of view these languages
suffer the following shortcomings. None of them (perhaps with an exception of
languages based on DL) makes it possible to express modalities (what is necessary and
what is contingent), to distinguish three kinds of context, viz. extensional level of
objects like individuals, numbers, functions (-in-extension), intensional level of
properties, propositions, offices and roles, and finally hyperintensional level of
concepts (i.e. algorithmically structured procedures). Concepts of n-ary relations are
unreasonably modelled by properties. True, each n-ary relation can be expressed by n
unary relations (properties) but such a representation is misleading and
incomprehensible. Ontology language should be, however, universal, highly expressive,
with transparent semantics and meaning driven axiomatisation.
For these reasons we vote for an expressive system of Transparent Intensional
Logic (TIL). From the formal point of view, TIL is a hyper-intensional, partial, typed
O-calculus. Hyperintensional, because we apply top-down approach to semantics, from
hyper-intensional (conceptual) level of procedures, via intensional down to extensional
level of abstraction. Basic semantic construct is an abstract procedure known as TIL
construction. Since TIL has been referred to in numerous EJC papers, in the next
paragraph we only briefly recapitulate basic principles of TIL. For the most up-to-date
exposition, see [5] and also [10].
M. Duží et al. / Ontology As a Logic of Intensions 5](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-19-320.jpg)
![1.2. A brief introduction to TIL
TIL is an overarching semantic theory for all sorts of discourse, whether colloquial,
scientific, mathematical or logical. The theory is a procedural one, according to which
sense is an abstract, pre-linguistic procedure detailing what operations to apply to what
procedural constituents to arrive at the product (if any) of the procedure. Such
procedures are rigorously defined as TIL constructions. The semantics is entirely anti-
contextual and compositional and it is, to the best of our knowledge, the only one that
deals with all kinds of context in a uniform way. Thus the sense of a sentence is an
algorithmically structured construction of the proposition denoted by the sentence. The
denoted proposition is a flat, or unstructured, mapping with domain in a logical space
of possible worlds. Our motive for working ‘top-down’ has to do with anti-
contextualism: any given unambiguous term or expression (even one involving
indexicals or anaphoric pronouns) expresses the same construction as its sense
whatever sort of context the term or expression is embedded within. And the meaning
of an expression determines the respective denoted entity (if any), but not vice versa.
The denoted entities are (possibly 0-ary) functions understood as set-theoretical
mappings. Thus we strictly distinguish between a procedure (construction) and its
product (here, a constructed function), and between a function and its value.
Intuitively, construction C is a procedure (a generalised algorithm). Constructions
are structured in the following way. Each construction C consists of sub-instructions
(constituents), each of which needs to be executed when executing C. Thus a
specification of a construction is a specification of an instruction on how to proceed in
order to obtain the output entity given some input entities.
There are two kinds of constructions, atomic and compound (molecular). Atomic
constructions (Variables and Trivializations) do not contain any other constituent but
themselves; they specify objects (of any type) on which compound constructions
operate. The variables x, y, p, q, …, construct objects dependently on a valuation; they
v-construct. The Trivialisation of an object X (of any type, even a construction), in
symbols 0
X, constructs simply X without the mediation of any other construction.
Compound constructions, which consist of other constituents as well, are Composition
and Closure. Composition [F A1…An] is the operation of functional application. It v-
constructs the value of the function f (valuation-, or v-, -constructed by F) at a tuple
argument A (v-constructed by A1, …, An), if the function f is defined at A, otherwise the
Composition is v-improper, i.e., it fails to v-construct anything.4
Closure [Ox1…xn X]
spells out the instruction to v-construct a function by abstracting over the values of the
variables x1,…,xn in the ordinary manner of the O-calculi. Finally, higher-order
constructions can be used twice over as constituents of composite constructions. This is
achieved by a fifth construction called Double Execution, 2
X, that behaves as follows:
If X v-constructs a construction X’, and X’ v-constructs an entity Y, then 2
X v-constructs
Y; otherwise 2
X is v-improper, failing as it does to v-construct anything.
TIL constructions, as well as the entities they construct, all receive a type. The
formal ontology of TIL is bi-dimensional; one dimension is made up of constructions,
the other dimension encompasses non-constructions. On the ground level of the type
hierarchy, there are non-constructional entities unstructured from the algorithmic point
of view belonging to a type of order 1. Given a so-called epistemic (or objectual) base
4
As mentioned above, we treat functions as partial mappings, i.e., set-theoretical objects, unlike the
constructions of functions.
M. Duží et al. / Ontology As a Logic of Intensions
6](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-20-320.jpg)
![of atomic types (R-truth values, L-individuals, W-time moments / real numbers, Z-
possible worlds), the induction rule for forming functional types is applied: where D,
E1,…,En are types of order 1, the set of partial mappings from E1 u…u En to D, denoted
‘(D E1…En)’, is a type of order 1 as well.5
Constructions that construct entities of order
1 are constructions of order 1. They belong to a type of order 2, denoted ‘*1’. The type
*1 together with atomic types of order 1 serves as a base for the induction rule: any
collection of partial mappings, type (D E1…En), involving *1 in their domain or range is
a type of order 2. Constructions belonging to a type *2 that identify entities of order 1
or 2, and partial mappings involving such constructions, belong to a type of order 3.
And so on ad infinitum.
The sense of an empirical expression is a hyperintension that is a construction that
produces a (possible world) D-intension, where D-intensions are members of type (DZ),
i.e., functions from possible worlds to an arbitrary type D. On the other hand, D-
extensions are members of a type D, where D is not equal to (EZ) for any E, i.e.,
extensions are functions whose domain is not the set of possible worlds.
Intensions are frequently functions of a type ((DW)Z), i.e., functions from possible
worlds to chronologies of the type D (in symbols: DWZ), where a chronology is a
function of type (DW).
Some important kinds of intensions are:
Propositions, type RWZ. They are denoted by empirical sentences.
Properties of members of a type D, or simply D-properties, type (RD)WZ.6
General terms,
some substantives, intransitive verbs (‘student’, ‘walks’) denote properties, mostly of
individuals.
Relations-in-intension, type (RE1…Em)WZ. For example transitive empirical verbs (‘like’,
‘worship’), also attitudinal verbs denote these relations.
D-roles, also D-offices, type DWZ, where D (RE). Frequently LWZ. Often denoted by
concatenation of a superlative and a noun (‘the highest mountain’).
An object A of a type D is denoted ‘A/D’. That a construction C/ n v-constructs an
object of type D is denoted ‘C ov D’. We use variables w and t as v-constructing
elements of type Z (possible worlds) and W (times), respectively. If C ov DWZ v-
constructs an D-intension, the frequently used Composition of the form [[Cw]t], the
intensional descent of the D-intension, is abbreviated ‘Cwt’.
The analysis of a sentence consists in discovering the logical construction
(procedure) encoded by a given sentence. To this end we apply a method of analysis
that consists of three steps:7
1) Type-theoretical analysis, i.e., assigning types to the objects that receive mention
in the analysed sentence.
2) Synthesis, i.e., combining the constructions of the objects ad (1) in order to
construct the proposition of type RWZ denoted by the whole sentence.
3) Type-Theoretical checking.
5
TIL is an open-ended system. The above epistemic base {R, L, W, Z} was chosen, because it is apt for
natural-language analysis, but the choice of base depends on the area and language to be analysed. For
instance, possible worlds and times are out of place in case of mathematics, and the base might consist of,
e.g., R and Q, where Q is the type of natural numbers.
6
We model D-sets and (D1…Dn)-relations by their characteristic functions of type (RD), (RD1…Dn),
respectively. Thus an D-property is an empirical function that dependently on states-of-affairs (WZ) picks-up a
set of D-individuals, the population of the property.
7
For details see, e.g.,[12].
M. Duží et al. / Ontology As a Logic of Intensions 7](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-21-320.jpg)
![To illustrate the method, let us analyse the sentence “All drivers are persons”.
Ad (1) The objects mentioned by the sentence are individual properties of being a
Driver and being a Person, and the quantifier All. Individual properties receive the type
(((RL)W)Z), RWZ for short. Given a world-time pair ¢w, t², a property applied to world w
and time t returns a class of individuals, its population at ¢w, t². Yet the sentence does
not mention any particular individual, be it a driver or a person. It says that the
population of drivers is a subset of persons. Thus the type of the (restricted) quantifier
All is ((R(RL))(RL)). Given a set M/(RL) of individuals, the quantifier All returns all the
supersets of M. Thus we have [0
All 0
M] o (R(RL)).
Ad (2) Now we combine constructions of the objects ad (1) in order to construct the
proposition (of type RWZ) denoted by the whole sentence. Since we aim at discovering
the literal analysis of the sentence, objects denoted by semantically simple expressions
‘driver’, ‘person’ and ‘all’ are constructed by their Trivialisations: 0
Driver, 0
Person,
0
All. By Composing these constructions, we obtain a truth-value (T or F), according as
the population of people belongs to the set of supersets of the population of drivers.
Thus we have, [[0
All 0
Driverwt] 0
Personwt] ov R. Finally, by abstracting over the values
of the variables w and t, we construct the proposition:
OwOt [[0
All 0
Driverwt] 0
Personwt].
Ad (3). By drawing a type-theoretical structural tree, we check whether particular
constituents of the above Closure are combined in a type-theoretically correct way.
Ow Ot [[0
All 0
Driverwt] 0
Personwt]
((R(RL))(RL)) (RL)
(R(RL)) (RL)
R
(RW)
((RW)Z) the type of a proposition, RWZ for short.
So much for the method of analysis and the semantic schema of TIL.
1.3. Ontology content
Formal ontology is a result of the conceptualization of a given domain. It contains
definitions of the most important entities, forms a conceptual hierarchy together with
the most important attributes and relations between entities. Material individuals are
mereological sums of other individuals, but only contingently so. Similarly, values of
attributes and properties are ascribed to individuals contingently, provided a given
property is purely contingent, that is without an essential core. Thus we advocate for a
(modest) individual anti-essentialism. On the other hand, on the intensional level of
propositions, properties, offices and roles, that is entities which we call ‘intensions’, the
most important relation to be observed is that of requisite. For instance, the property of
being a mammal is a requisite of the property of being a whale. It is an analytically
necessary relation between intensions that gives rise to the so-called ISA hierarchy.
Thus on the intensional level we advocate for intensional essentialism; an essence of a
M. Duží et al. / Ontology As a Logic of Intensions
8](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-22-320.jpg)
![property is the set of all its requisites. Finally, on the hyper-intensional level of
concepts, relations to be observed are equivalence (i.e. producing the same entity),
refinement (a compound concept is substituted for a simpler yet equivalent concept),
entailment and presupposition.
The structure of ontology building starts on the hyper-intensional level with the
specification of primitive concepts. Next we specify compound concepts as ontological
definitions of entities of a given domain. Having defined entities, we can specify their
most important descriptive attributes. The building process continues by specifying
particular (empirical) relations between entities and analytical relations of requisites
that serve to build up ontological hierarchy. Finally, the most important general rules
that govern behaviour of the system are specified. Here again we distinguish
analytically necessary constraints from nomic and common necessities that are given
by laws and conventions, respectively; they are not valid analytically necessary. For
instance, mathematical laws are analytically necessary, they hold independently of
states of affairs. On the other hand, laws of physics are not logically or analytically
necessary, they are only nomically necessary. It is even disputable whether these laws
are eternal in our world. Yet still weaker constraints are, for instance, traffic laws. That
we drive on the right-hand side of a lane is valid only by convention and locally.
Summarising, basic parts of a formal ontology should encompass:
(1) Conceptual (terminological) dictionary which contains:
a) primitive concepts
b) compound concepts (ontological definitions of entities)
c) the most important descriptive attributes, in particular identification of entities
(2) Relations
a) contingent empirical relations between entities, in particular the part-whole
relation
b) analytical relations between intensions, i.e., requisites and essence, which give
rise to ISA hierarchy
(3) Integrity constraints
a) Analytically necessary rules
b) Nomologically necessary rules
c) Common rules of ‘necessity by convention’
Concerning ad (1), in particular ontological definitions, this topic has been dealt
with in [4]. Briefly, ontological definition of an entity is a compound construction of
the entity. Such a definition often serves as a refinement of a primitive concept of the
entity, which makes it possible to prove some analytic statements about the entity. For
example, the sentence “Whales are not dolphins” contains the empirical predicates ‘is a
whale’ and ‘is a dolphin’, yet the sentence is analytic truth. At no world/time are the
properties being a whale and being a dolphin co-instantiated by the same individual.
The proposition constructed by the sentence is the necessary proposition TRUE. In order
to prove it, we need to refine the concept of a whale. To this end we make use of the
fact that the property of being a whale can be defined as the property of being a marine
mammal of the order Cetacea that is neither a dolphin nor a porpoise.8
Thus the
ontological definition of the property of being a whale is
8
See, for instance, http://mmc.gov/species/speciesglobal.html#cetaceans or
http://www.crru.org.uk/education/factfiles/taxonomy.htm
M. Duží et al. / Ontology As a Logic of Intensions 9](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-23-320.jpg)
![OwOt Ox [[0
Mammalwt x] š [0
Marinewt x] š [0
Cetaceawt x] š
™[0
Dolphinwt x] š ™[0
Porpoisewt x]]
Types: x o L; Cetacea, Mammal, Marine, Dolphin, Porpoise/(RL)WZ.
Using this definition instead of the primitive concept 0
Whale we get:
OwOt [0
No Ox [[0
Mammalwt x] š [0
Marinewt x] š [0
Cetaceawt x] š ™[0
Dolphinwt x] š
™[0
Porpoisewt x]] 0
Dolphinwt].
Gloss: “No individual x such that x is a marine mammal of the order Cetacea and x is
neither a dolphin nor a porpoise is a dolphin”.
In this paper we focus problems ad (2) and (3), that is, we will examine relations
between intensions, properties of intensions and various integrity constraints viewed
via the logic of intensions.
2. Logic of intensions
2.1. Requisites and ISA hierarchies.
It is important to distinguish between purely contingent propositions and the
proposition TRUE that takes the value T in all ¢w, t²-pairs. The latter is denoted by
analytically true sentences such as the above analysed sentence “No whale is a
dolphin” or “All drivers are persons”. We have seen that the literal analysis does not
make it possible to prove the analytic truth of the sentence. To this end we have to
possibilities. Either we can record ontological definitions refining the primitive
concepts of the objects talked about (as illustrated by the above whale-example), or we
need to explicitly record in our ontology the fact that there is a necessary relation (-in-
extension) between the two properties. We call this relation a requisite, in this case
Req1/(R(RL)WZ(RL)WZ) and it receives this definition:
[0
Req1
0
Person 0
Driver] =df wt [x [[0
Driverwt x] Š [0
Personwt x]]]
Gloss. Being a person is a requisite of being a driver. In other words, necessarily and
for any individual x, if x instantiates the property of being a driver then x also
instantiates the property of being a person.
Now we set out the logic of requisites, because this relation is the basic relation
that gives rise to ISA taxonomies.9
The requisite relations Req are a family of relations-
in-extension between two intensions, hence of the polymorphous type (RDWZEWZ), where
possibly D = E. The relation of a requisite can be defined between intensions of any
type. For instance, a requisite of finding is the existence of a sought object. Infinitely
many combinations of Req are possible, but the following four are the relevant ones we
wish to consider:
(1) Req1 /(R (RL)WZ (RL)WZ): an individual property is a requisite of another such
property.
(2) Req2 /(R LWZ LWZ): an individual office is a requisite of another such office.
(3) Req3 /(R (RL)WZ LWZ): an individual property is a requisite of an individual office.
(4) Req4 /(R LWZ (RL)WZ): an individual office is a requisite of an individual property.
9
Parts of this section draw on material presented in [5], Chapter 4.
M. Duží et al. / Ontology As a Logic of Intensions
10](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-24-320.jpg)
![Neglecting complications due to partiality, definitions of particular kinds of requisites
should be obvious: “Y is a requisite of X” iff “necessarily whatever occupies/
instantiates X at ¢w, t² it also occupies/instantiates Y at this ¢w, t².”
Examples. Being a Person and being a Driver is an example of Req1. An example of
Req2 is The Commander-in-Chief and the President of USA. The former office is a
requisite of the latter, such that whoever is the President is also the Commander-in-
Chief. However, it may happen that the Presidency goes vacant, while somebody
occupies the office of Commander-in-Chief. As an example of Req3 we can adduce the
property of being a US citizen and the office President of USA. Finally, an example of
Req4 is the pair of God-office and the property of being Omniscient.
Note that while Req1/(R(RL)WZ(RL)WZ) and Req2/(RLWZLWZ) are homogeneous, Req3,
Req4 are heterogeneous. Since the latter two do not have a unique domain, it is not
sensible to ask what sort of ordering they are. Not so with the former two. We define
them as quasi-orders (a.k.a. pre-orders) over (R(RL)WZ), (RLWZ), respectively, that can be
strengthened to weak partial orderings. However, they cannot be strengthened to strict
orderings on pain of paradox, since they would then both be reflexive and irreflexive.
We wish to retain reflexivity, such that any intension having requisites will count itself
among its requisites.
Since intensions are properly partial functions, in order to deal with partiality we
make use of three properties of propositions True, False, Undef/(RRWZ)WZ. If P o RWZ is
a construction of a proposition, [0
Truewt P] returns T if the proposition takes the truth-
value T in a given ¢w, t², otherwise F. [0
Falsewt P] returns T if the proposition takes the
truth-value F in a given ¢w, t², otherwise F. [0
Undefwt P] returns T in a given ¢w, t² if
neither [0
Truewt P] nor [0
Falsewt P] returns T, otherwise F.
Claim 1 Req1 is a quasi-order on the set of L-properties.
Proof. Let X, Y o (RL)WZ. Then Req1 belongs to the class QO/(R(R(RL)WZ(RL)WZ)) of
quasi-orders over the set of individual properties:
Reflexivity. [0
Req1 X X] =
wt [x [[0
Truewt OwOt [Xwt x]] Š [0
Truewt OwOt [Xwt x]]]]
Transitivity. [[[0
Req1 Y X] š [0
Req1 Z Y]] Š [0
Req1 Z X]] =
[wt [x [[0
Truewt OwOt [Xwt x]] Š [0
Truewt OwOt [Ywt x]]] š
[[0
Truewt OwOt [Ywt x]] Š [0
Truewt OwOt [Zwt x]]]] Š
wt [x [[0
Truewt OwOt [Xwt x]] Š [0
Truewt OwOt [Zwt x]]]]]
In order for a requisite relation to be a weak partial order, it will need to be also
anti-symmetric. The Req1 relation is, however, not anti-symmetric. If properties X, Y
are mutually in the Req1 relation, i.e., if
[[0
Req1 Y X] š [0
Req1 X Y]]
then at each ¢w, t² the two properties are truly ascribed to exactly the same individuals.
This does not entail, however, that X, Y are identical. It may be the case that there is an
individual a such that [Xwt a] v-constructs F whereas [Ywt a] is v-improper. For instance,
the following properties X, Y differ only in truth-values for those individuals who never
M. Duží et al. / Ontology As a Logic of Intensions 11](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-25-320.jpg)
![smoked (let StopSmoke/(RL)WZ: the property of having stopped smoking).10
Whereas X
yields truth-value gaps on such individuals, Y is false of them:
X = OwOt Ox [0
StopSmokewt x]
Y = OwOt Ox [0
Truewt OwOt [0
StopSmokewt x]].
In order to abstract from such an insignificant difference, we introduce the
equivalence relation Eq/(R(RL)WZ(RL)WZ) on the set of individual properties; p, q o
(RL)WZ; =/(RRR):
0
Eq = Opq [x [[0
Truewt OwOt [pwt x]] = [0
Truewt OwOt [qwt x]]]].
Now we define the Req1’ relation on the factor set of the set of L-properties as
follows. Let [p]eq = Oq [0
Eq p q] and [Req1’ [p]eq [q]eq] = [Req1 p q]. Then:
Claim 2 Req1’ is a weak partial order on the factor set of the set of L-properties with
respect to Eq.
Proof. It is sufficient to prove that Req1’ is well-defined. Let p’, q’ be L-properties such
that [0
Eq p p’] and [0
Eq q q’]. Then
[Req1’ [p]eq [q]eq] = [Req1 p q] =
wt [x [[0
Truewt OwOt [pwt x]] Š [0
Truewt OwOt [qwt x]]]] =
wt [x [[0
Truewt OwOt [p’wt x]] Š [0
Truewt OwOt [q’wt x]]]] = [Req1’ [p’]eq [q’]eq].
Now obviously the relation Req1’ is antisymmetric:
[[0
Req1’ [p]eq [q]eq] š [0
Req1’ [q]eq [p]eq]] Š [[p]eq = [q]eq].
Claim 3 Req2 is a weak partial order defined on the set of L-offices.
Proof. Let X, Y o LWZ. Then the Req2 relation belongs to the class WO/(R(R LWZLWZ)) of
weak partial orders over the set of individual offices.
Reflexivity. [0
Req2 X X] = [wt [[0
Occwt X] Š [0
Truewt OwOt [Xwt = Xwt]]]].
Antisymmetry. [[[0
Req2 Y X] š [0
Req2 X Y]] Š [X = Y]] =
[wt [[[0
Occwt X] Š [0
Truewt OwOt [Xwt = Ywt]]] š
[[0
Occwt Y] Š [0
Truewt OwOt [Xwt = Ywt]]]] Š [X = Y]]
Transitivity. [[[0
Req2 Y X] š [0
Req2 Z Y]] Š [0
Req2 Z X]] =
[wt [[[0
Occwt X] Š [0
Truewt OwOt [Xwt = Ywt]]] š
[[0
Occwt Y] Š [0
Truewt OwOt [Ywt = Zwt]]]] Š
wt [[0
Occwt X] Š [0
Truewt OwOt [Xwt = Zwt]]]].
Remark. Antisymmetry requires the consistent identity of the offices constructed by X,
Y: [X = Y]. The two offices are identical iff at all worlds/times they are either co-
10
We take the property of having stopped smoking as presupposing that the individual previously
smoked. For instance, that Tom stopped smoking can be true or false only if Tom was once a smoker.
Similarly for the property of having stopped whacking one’s wife.
M. Duží et al. / Ontology As a Logic of Intensions
12](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-26-320.jpg)
![occupied by the same individual or are both vacant: wt [[0
Truewt OwOt [Xwt = Ywt]] ›
[0
Undefwt OwOt [Xwt = Ywt]]] = wt ™[0
Falsewt OwOt [Xwt = Ywt]], which is the case here.
It is a well-known fact that hierarchies of intensions based on requisite relations
establish inheritance of attributes and possibly also of operations. For instance, a driver
in addition to his/her special attributes like having a driving license inherits all the
attributes of a person. This is another reason for including such a hierarchy into
ontology. This concludes our definition of the logic of the requisite relations. We turn
now to dealing with a part-whole relation.
2.2. Part-whole relation
We advocate for the thesis of modest individual anti-essentialism: If an individual
I has a property P necessarily (i.e., in all worlds and times), then P is a constant or
partly constant function. In other words, the property has a non-empty essential core
Ess, where Ess is a set of individuals that have the property necessarily, and I is an
element of Ess.
There is, however, a frequently voiced objection to individual anti-essentialism. If,
for instance, Tom’s only car is disassembled into its elementary physical parts, then
Tom’s car no longer exists; hence, the property of being a car is essential of the
individual referred to by ‘Tom’s only car’. Our response to the objection is this. First,
what is denoted (as opposed to referred to) by ‘Tom’s only car’ is not an individual,
but an individual office/role, which is an intension of type LWZ having occasionally
different individuals, and occasionally none, as values in different possible worlds at
different times. Whenever Tom does buy a car, it is not logically necessary that Tom
buy some one particular car rather than any other. Second, the individual referred to as
‘Tom’s only car’ does not cease to exist even after having been taken apart into its
most elementary parts. It has simply lost some properties, among them the property of
being a car, the property of being composed of its current parts, etc, while acquiring
some other properties. Suppose somebody by chance happened to reassemble the parts
so that the individual would regain the property of being a car. Then Tom would have
no right to claim that this individual was his car, in case it was allowed that the
individual had ceased to exist. Yet Tom should be entitled to claim the reassembled car
as his.11
Therefore, when disassembled, Tom’s individual did not cease to exist; it had
simply (unfortunately) obtained the property of completely disintegrating into its
elementary physical parts. So much for modest individual anti-essentialism.
The second thesis we are going to argue for is this. A material entity that is a
mereological sum of a number of parts, such as a particular car, is from a logical
point of view a simple, hence unstructured individual. Only its design, or
construction, is a complex entity, namely a structured procedure. This is to say that a
car is not a structured whole that organizes its parts in a particular manner. Tichý says:
[A] car is a simple entity. But is this not a reductio ad absurdum? Are cars not complex, as
anyone who has tried to fix one will readily testify?
No, they are not. If a car were a complex then it would be legitimate to ask: Exactly how
complex is it? Now how many parts does a car consist of? One plausible answer which may
suggest itself is that it has three parts: an engine, a chassis, and a body. But an equally plausible
answer can be given in terms of a much longer list: several spark plugs, several pistons, a
11
As Tichý argues in [16], where he uses the example of a watch being ‘repaired’ by a watchmaker in
such a way as to become a key.
M. Duží et al. / Ontology As a Logic of Intensions 13](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-27-320.jpg)
![starter, a carburettor, four tyres, two axles, six windows, etc. Despite being longer the latter list
does not overlap with the former: neither the engine, nor the chassis nor the body appears on it.
How can that be? How can an engine, for example, both be and not be a part of one and the
very same car?
There is no mystery, however. It is a commonplace that a car can be decomposed in several
alternative ways. … Put in other words, a car can be constructed in a very simple way as a
mereological sum of three things, or in a more elaborate way as a mereological sum of a much
larger set of things. ([17], pp. 179-80.)
It is a contingent fact that this or that individual consists of other individuals and
thereby creates a mereological sum. Importantly, being a part of is a relation between
individuals, not between intensions. There can be no inheritance or implicative relation
between the respective properties ascribed to a whole and its individual parts. Thus it is
vital not to confuse the requisite relation, which obtains between intensions, with the
part-whole relation, which obtains between individuals. The former relation obtains of
necessity (e.g., necessarily, any individual that is an elephant is a mammal), while the
latter relation obtains contingently. Logically speaking, any two individuals can enter
into the part-whole relation. One possible combination has Saturn a part of Socrates (or
vice versa). There will be restrictions on possible combinations, but these restrictions
are anchored to nomic necessity (provided a given possible world at which a
combination of individuals is attempted has laws of nature at all). One impossible
combination would have the largest mountain on Saturn be a part of S (or vice versa).
Why impossible? Because of wrong typing: the arguments of the part-whole relation
must be individuals (i.e., entities of type L), but the largest mountain on Saturn is an
individual office while S is a real number.
Yet there is another question interesting from the ontological point of view: which
parts are essential for an individual in order to have a property P? For instance, the
property of having an engine is essential for the property of being a car, because
something designed without an engine does not qualify as a car, but at most as a toy
car, which is not a car. The answer to the question which parts are essential in order to
have a property P is, in the car/engine example, that the property of having an engine is
a requisite of the property of being a car. What is necessary is that a car, any car,
should have an engine. It is even necessary that it should have a particular kind of
engine, where being a kind of engine is a property of a property of individuals. This
kind of a requisite relation should be also included into ontology.
What is not necessary is that any car should have some one particular engine
belonging to a particular kind of engine: mutatis mutandi, any two members of a
particular kind of engine will be mutually replaceable.12
Thus the relation Part_of is of
type (RLL)WZ.
2.3. Some other properties of intensions
In addition to the above described higher-degree relations of requisite it is also useful
to include into ontology some other higher-degree relations between and properties of
intensions. In particular, we examine properties of relations-in-intension. For instance,
that a given relation is necessarily reflexive, anti-symmetric and transitive, like the
partial order induced by a requisite relation.
12
This problem is connected with the analysis of property modification, including being a malfunctioning P.
M. Duží et al. / Ontology As a Logic of Intensions
14](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-28-320.jpg)
![These higher-order properties of intensions are necessarily valid due to the way they
are constructed. Since we explicate concepts as closed constructions modulo D- and K-
transformation, we can also speak about mutual relations between and properties of
concepts which define particular intensions. Those that deserve our attention are in
particular:
Incompatibility of concepts defining particular properties, i.e., the respective
populations are necessarily disjoint; example: bachelor vs. married man.
Equivalence of concepts, i.e., the defined properties are one and the same property
Week-equivalence of concepts, i.e., the defined properties are ‘almost the same’; as
an example we echo the relation Eq between individual properties defined in the
previous paragraph
Functionality of a relation-in-intension, that is necessarily, in each ¢w, t²-pair, a
given relation R Ž Awt uBwt is a mapping fR
: Awt Æ Bwt assigning to each element of
A at most one element of B
Inverse functionality of a relation-in-intension, that is necessarily, in each ¢w, t²-
pair, a given relation-in-extension R Ž Awt u Bwt is a mapping fR–1
: Bwt Æ Awt
assigning to each element of Bwt at most one element of Awt.
We also often need to specify some restrictions on the domain or range of a given
mapping. Such local restrictions are specified as integrity constraints which we are
going to deal with in the next paragraph.13
2.4. Integrity constraints
Classical integrity constraints specify whether a given function-in-intension (i.e. an
attribute) must be singular or may be multi-valued, and whether it is mandatory or
optional. These constraints are analytically necessary. As an example of a cardinality
constraint we can adduce the constraint that everybody has just one (biological) mother
and father. That each order must concern a customer, a producer/seller and some
products is an example of a constraint on mandatory relation.
In addition to these analytical constraints it is useful to specify restrictions on
cardinality in case of multi-valued attributes, or particular roles of individuals that enter
into a given relation, etc. These constraints have the character of nomically necessary
constraints given by some conventions valid in a given domain. For instance, there can
be a constraint valid in a given organization that each exporter can have five customers
at maximum.
Regardless of the character of a given domain, we should always specify the
degree of necessity of a given integrity constraint. If C ov R v-constructs the respective
condition to be met, the basic kinds of constraints ordered from the highest to the
lowest are:
a) Analytically necessary rules; these are specified by constructions of the form
wt C.
b) Nomologically necessary rules; these are specified by constructions of the
form Owt C.
13
In the terminology of standard ontology languages, the so-called “properties” are actually relations-
in-intension with ‘slots’. Thus we can speak about ‘slot constraints’ and facets that are local slot constraints.
See [15].
M. Duží et al. / Ontology As a Logic of Intensions 15](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-29-320.jpg)
![c) Common rules of ‘necessity by convention’; these are specified by
constructions of the form OwOt x [C …x …].
To adduce an example, imagine a mobile agent (typically a car) that encounters an
obstacle on his way. In order to specify the behaviour of the agent properly, we must
take into account priorities of particular constraints. First, the agent must take into
account analytical constraints like that there cannot be two material objects at the same
position at the same time. Second, physical laws must be considered; for instance, we
must calculate vehicle stopping distance taking into account the speed of the agent as
well as of the obstacle and the direction of their move. Only then conventional laws
like traffic rules can be considered. If the agent comes to a conclusion that the stopping
distance is greater than the distance of an obstacle then, of course, the rules like driving
on the right-hand side of a lane or traffic sings cannot be followed.
So much for the logic of intensions. In the next section we tackle another important
phenomenon that is useful to include into ontology so that reasoning of agents can be
properly specified, namely two kinds of entailment relation which also can be viewed
as higher-order integrity constraints. They are presupposition vs. mere entailment.
3. Presupposition and entailment
When used in a communicative act, a sentence communicates something (the focus F)
about something (the topic T). Thus the schematic structure of a sentence is F(T). The
topic T of a sentence S is often associated with a presupposition P of S such that P is
entailed both by S and non-S. On the other hand, the clause in the focus usually triggers
a mere entailment of some P by S. Schematically,
(i) S |= P and non-S |= P (P is a presupposition of S);
Corollary: If non-P then neither S nor non-S is true.
(ii) S |= P and neither (non-S |= P) nor (non-S |= non-P) (mere entailment).
More precisely, the entailment relation obtains between hyperpropositions P, S, i.e.,
the meaning of P is entailed or presupposed by the meaning of S. For the precise
definition of entailment and presupposition, see [5], Section 1.5.
The phenomenon of topic-focus is associated de dicto – de re ambivalence.
Consider a pair of sentences differing only in terms of topic-focus articulation:
(1) The critical situation on the highway D1 was caused by the agent a.
(2) The agent a caused the critical situation on the highway D1.
While (1) not only entails but also presupposes that there be a critical situation on D1,
the truth-conditions of (2) are different, as our analysis clarifies.
First, (1) as well as (1’),
(1’) The critical situation on the highway D1 was not caused by the agent a.
are about the critical situation, and that there is a such a situation is not only entailed
but also presupposed by both the sentences.
As we have seen above, the meaning of a sentence is a procedure producing a
proposition, i.e. an object of type RWZ. Execution of this procedure in any world/time
yields a truth-value T, F or nothing. Thus we can conceive the sense of a sentence as an
M. Duží et al. / Ontology As a Logic of Intensions
16](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-30-320.jpg)
![instruction on how to evaluate its truth-conditions in any world/time. The instruction
encoded by (1) formulated in logician’s English is this:
If there is a critical situation on the highway D1 then return T or F according as the
situation was caused by the agent a, else fail (to produce a truth-value).
Applying our method of analysis introduced in Section 1, we start with assigning
types to the objects that receive mention in the sentence. Simplifying a bit let the
objects be: Crisis/RWZ: the proposition that there is a critical situation on the highway
D1; Cause/(RLRWZ)WZ: the relation-in-intension between an individual and a proposition
which has been caused to be true by the individual; Agent_a/L.
A schematic analysis of (1) comes down to this procedure:
(1s
) OwOt [if 0
Crisiswt then [0
Causewt
0
Agent_a 0
Crisis] else Fail]
So far so good; yet there is a problem of how to analyse the connective if-then-else.
There has been much dispute over the semantics of ‘if-then-else’ among computer
scientists. We cannot simply apply material implication, Š. For instance, it might seem
that the instruction expressed by “If 5=5 then output 1, else output the result of 1
divided by 0” received the analysis
[[[0
5=0
5] Š [n=0
1]] š [™[0
5=0
5] Š [n=[0
Div 0
1 0
0]]]],
where n is the output number. But the output of the above procedure should be the
number 1 because the else clause is never executed. However, due to the strict principle
of compositionality that TIL observes, the above analysis fails to produce anything, the
construction being improper. The reason is this. The Composition [0
Div 0
1 0
0] does not
produce anything: it is improper because the division function takes no value at the
argument 1, 0. Thus the Composition [n = [0
Div 0
1 0
0]] is v-improper for any
valuation v, because the identity relation = does not receive an argument, and so any
other Composition containing the improper Composition [0
Div 0
1 0
0] as a constituent
also comes out v-improper. The underlying principle is that partiality is being strictly
propagated up. This is the reason why the if-then-else connective is often said to be a
non-strict function.
However, there is no cogent reason to settle for non-strictness. We suggest
applying a mechanism known in computer science as lazy evaluation. The procedural
semantics of TIL operates smoothly even at the level of constructions. Thus it enables
us to specify a strict definition of if-then-else that meets the compositionality constraint.
The analysis of “If P then C1, else C2” is a procedure that decomposes into two phases.
First, on the basis of the condition P ov R, select one of C1, C2 as the procedure to be
executed. Second, execute the selected procedure.
The first phase, viz. the selection, is realized by the Composition
[0
the_only Oc [[P Š [c=0
C]] š [™P Š [c=0
D]]]].
The Composition [[P Š [c=0
C]] š [™P Š [c=0
D]]] v-constructs T in two cases. If
P v-constructs T then the variable c receives as its value the construction C, and if P v-
constructs F then the variable c receives the construction D as its value. In either case
the set v-constructed by Oc [[P Š [c=0
C]] š [™P Š [c=0
D]]] is a singleton. Applying
the singulariser the_only to this set returns as its value the only member of the set, i.e.,
either the construction C or D.
M. Duží et al. / Ontology As a Logic of Intensions 17](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-31-320.jpg)
![Second, the chosen construction c is executed. As a result, the schematic analysis
of “If P then C else D” turns out to be
(*) 2
[0
L Oc [[P Š [c=0
C]] š [™P Š [c=0
D]]]].
Types: PoR (the condition of the choice between the execution of C or D); C, D/ n;
variable c ov n; the_only/( n(R n)): the singulariser function that associates a singleton
set of constructions with the only construction that is an element of this singleton, and
which is otherwise (i.e., if the set is empty or many-valued) undefined.
Note that we do need a hyperintensional, procedural semantics here. First of all,
we need a variable c ranging over constructions. Moreover, the evaluation of the first
phase does not involve the execution of the constructions C and D. These constructions
are only arguments of other constructions.
Returning to the analysis of (1), in our case the condition P is that there be a crisis
on the highway D1, i.e., 0
Crisiswt. The construction C that is to be executed if P yields
T is [0
Causewt
0
Agent_a 0
Crisis]], and if P yields F then no construction is to be
selected. Thus the analysis of the sentence (1) comes down to this Closure:
(1*) OwOt 2
[0
LOc [[0
Crisiswt Š [c = 0
[0
Causewt
0
Agent_a 0
Crisis]]]]
š [™0
Crisiswt Š 0
F]]]
The evaluation of (1*) in any ¢w, t²-pair depends on whether the presupposition
0
Crisiswt is true in ¢w, t². If true, then the singleton v-constructed by Oc [ … ] contains
as the only construction the Composition [0
Causewt
0
Agent_a 0
Crisis]], which is
afterwards executed to return T or F, according as the agent a caused the crisis. If false,
then the second conjunct in Oc […] comes down to [0
T Š 0
F] and thus we get Oc 0
F.
The v-constructed set is empty. Hence, 2
[LOc 0
F] is v-improper, that is the Double
Execution fails to produce a truth-value.
To generalise, an analytic schema of a sentence S associated with a presupposition
P is a procedure of the form
If P then S else Fail.
The corresponding schematic TIL construction is
(**) OwOt 2
[0
LOc [[Pwt Š [c=0
Swt]] š [™Pwt Š 0
F]]].
The truth-conditions of the other reading, i.e. the reading of (2)
(2) “The agent a caused the critical situation on the highway D1”
are different.
Now the sentence (2) is about the agent a (topic), ascribing to a the property that it
caused the crisis (focus). Thus the scenario of truly asserting that (2) is not true can be,
for instance, this. Though it is true that the agent a is known as a hit and run driver, this
time he behaved well and prevented a critical situation from arising. Or, a less
optimistic scenario is thinkable. The critical situation on D1 is not because of the agent
a’s risky driving but because the highway is in a very bad condition.
Hence, that there is a crisis is not presupposed by (2), and its analysis is this
Closure:
(2*) OwOt [0
Causewt
0
Agent_a 0
Crisis]
M. Duží et al. / Ontology As a Logic of Intensions
18](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-32-320.jpg)
![The moral we can extract from these examples is this. Logical analysis cannot
disambiguate any sentence, because it presupposes full linguistic competence. Thus we
should include into our formal ontology the schematic rules that accompany activities
like agents’ seeking and finding, causing something, etc. Then our fine-grained method
can contribute to a language disambiguation by making these hidden features explicit
and logically tractable. In case there are more non-equivalent senses of a sentence we
furnish the sentence with different TIL constructions. If an agent receives an
ambiguous message, he/she can answer by asking for disambiguation. Having a formal
fine-grained encoding of a sense, the agent can then infer the relevant consequences.
4. Conclusion
The theoretical specification of particular rules is only the first step. When making
these features explicit we keep in mind an automatic deduction that will make use of
these rules. To this end we currently develop a computational FIPA compliant variant
of TIL, the functional programming language TIL-Script (see [3]). The direction of
further research is clear. We are going to continue the development the TIL-Script
language in its full-fledged version equivalent to TIL calculus.
The development of TIL-Script is still a work in progress, in particular the
implementation of its inference machine. From the theoretical point of view, the
calculus and the rules of inference have been specified in [5], Sections 2.6 and 2.7. Yet
its full implementation is a subject of further research. Currently we proceed in stages.
First we implemented a method that decides a subset of the TIL-Script language
computable by Prolog (see [2]). This subset has been now extended to the subset
equivalent to standard FOL. For ontology building we combine traditional tools and
languages like OWL (Ontology Web Language) with TIL-Script. We developed an
extension of the editor Protégé-OWL so that to create an interface between OWL and
TIL-Script. The whole method has been tested within the project ‘Logic and Artificial
Intelligence for Multi-Agent Systems’ (see http://labis.vsb.cz/) using a traffic system as
a case study. The sample test contained five mobile agents (cars), three car parks and a
GIS agent. The GIS agents provided mobile agents with ‘visibility’, i.e., the
coordinates of the objects within their visibility. All the agents communicated in TIL-
Script and started with minimal (but not overlapping) ontologies. During the test they
learned new concepts and enriched their ontology in order to be able to meet their goals.
The agents’ goal was to find a vacant parking lot and park the car. All the agents
succeeded and parked in a few seconds, which proved that the method is applicable and
usable not only as an interesting theory but also in practice.
Acknowledgements.
This research has been supported by the Grant Agency of the Czech Republic, projects No.
401/09/H007 ‘Logical Foundations of Semantics’ and 401/10/0792, ‘Temporal aspects of
knowledge and information’, and by the internal grant agency of FEECS VSB-Technical
University Ostrava, project No. IGA 22/2009, ‘Modeling, simulation and verification of software
processes’.
M. Duží et al. / Ontology As a Logic of Intensions 19](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-33-320.jpg)
![References
[1] Baader, F., Calvanese, D., McGuinness, D., L., Nardi, D., and Patel-Schneider, P., F., editors. The
Description Logic Handbook: Theory, Implementation and Application. Cambridge University Press,
2002.
[2] íhalová, M., Ciprich, N., Duží, M., Menšík, M. (2009): Agents' reasoning using TIL-Script and Prolog.
In 19th
Information Modelling and Knowledge Bases, ed. T. Tokuda, Y. Kiyoki, H. Jaakkola, T. Welzer,
Družovec, Slovenia: University of Maribor, 137-156.
[3] Ciprich, N., Duží, M. and Košinár, M.: The TIL-Script language. In Kiyoki, Y., Tokuda, T. (eds.): EJC
2008, Tsukuba, Japan 2008, pp. 167-182.
[4] Duží, M., Materna, P. (2009): Concepts and Ontologies. In Information Modelling and Knowledge Bases
XX . Y. Kiyoki, T. Tokuda, H. Jaakola, X. Chen, N. Yoshida (eds.), Amsterdam: IOS Press, pp. 45-64.
[5] Duží, M., Jespersen, B. and P. Materna: Procedural Semantics for Hyperintensional Logic; Foundations
and Applications of Transparent Intensional Logic. Springer: series for Logic, Epistemology and the
Unity of Science, Vol. 17, 2010, ISBN: 978-90-481-8811-6.
[6] Gordon, M. J. C. and Melham, T. F. (eds.) 1993: Introduction to HOL: A Theorem Proving Environment
for Higher Order Logic. Cambridge: Cambridge University Press.
[7] Hayes, P., Menzel, C., 2001. Semantics of knowledge interchange format. In: IJCAI 2001 Workshop on
the IEEE Standard Upper Ontology.
[8] Horrocks, I. and Patel-Schneider, P.F. 2003: Three These of Representation in the Semantic Web.
WWW2003, May 20-24, Budapest, Hungary, 2003, (retrieved 10.1.2005) URL:
http://www2003.org/cdrom/papers/refereed/p050/p50-horrocks.html.
[9] Horrocks, I., Patel-Schneider, P.F., Boley, H., Tabet, S., Grosof, B. and Dean, M 2004: SWRL: A
Semantic Web Rule Language Combiming OWL and RuleML. W3C Member Submission, May 2004,
(retrieved 10.1.2010), URL: http://www.w3.org/Submission/SWRL/.
[10] Jespersen, B. (2008): ‘Predication and extensionalization’. Journal of Philosophical Logic, vol. 37, 479
– 499.
[11] Kifer, M., Lausen, G., and James Wu. Logical foundations of object-oriented and frame-based
languages. Journal of the ACM, 42(4):741-843, 1995.
[12] Materna, P. and Duží M. (2005): ‘The Parmenides principle’, Philosophia, 32, 155-80.
[13] Paulson. L. C. 1994: Isabelle: A Generic Theorem Prover. Number 828 in LNCS. Berlin: Springer.
[14] Sowa, John, F.: Knowledge Representation. Logical, Philosophical, and Computational Foundations.
Brooks/Cole 2000.
[15] Svátek, V. Ontologie a WWW. www source: http://nb.vse.cz/~svatek/onto-www.pdf
[16] Tichý, P. 1987. Individuals and their roles (in German; in Slovak in 1994). Reprinted in (Tichý 2004:
710-748).
[17] Tichý, P. 1995. Constructions as the subject-matter of mathematics. In The Foundational Debate:
Complexity and Constructivity in Mathematics and Physics, eds. W. DePauli-Schimanovich, E. Köhler
and F. Stadler, 175-185. Dordrecht, Boston, London, and Vienna: Kluwer. Reprinted in (Tichý 2004:
873-885).
[18] Tichý, P. 2004. Collected Papers in Logic and Philosophy, eds. V. Svoboda, B. Jespersen, C. Cheyne.
Prague: Filosofia, Czech Academy of Sciences, and Dunedin: University of Otago Press.
[19] W3C 2004: The World Wide Web Consortium: OWL Web Ontology Language Overview W3C
Recommendation 10 February 2004, (retrieved 10.1.2010) URL: http://www.w3.org/TR/owl-
features/.
M. Duží et al. / Ontology As a Logic of Intensions
20](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-34-320.jpg)
![purpose dependent of the community. In the current state, most sensor data are not used
effectively widely because each research community installs the sensor of each
research purpose. It is necessary to share the sensor data with the information on the
purpose of use and the background knowledge. For users in the other fields, it is
difficult to understand how the sensor data are related to their lives and what the sensor
data means. Generally, the expression of the sensor data is an enumeration of the
numerical values with domain-specific formatting. For making it possible to utilize
those data by other domain-specialists, it is important to show what the sensor data
mean and what influence the sensor data cause. Some methods of annotating and
connecting the sensor data are expected directly. However, it is too hard and complex.
An interpretation and utilization of the sensor data are different according to user's
background knowledge and his/her purposes. It is important to realize interconnection
mechanisms depending on user's background knowledge and his/her purpose for sensor
data.
Currently, we have organized a joint research with the Space Environment Group
of NICT, to solve how to share sensor data related to the space weather field. The aim
of this research is to create new applications of space-weather sensor-data by
combining the related knowledge resources. Space Environment Group of NICT is
delivering sensor data of solar activities and space environment that is called space
weather by RSS [1]. Space weather shows conditions on the Sun and in the solar wind,
magnetosphere, ionosphere, and thermosphere. These can endanger human life or
health by affecting the performance and reliability of space-borne and ground-based
man-made systems [2] such as communication failure, damage of electric devices for
space satellite, bombing, etc. The group is delivering these data so that various users
may use them.
In our current global environment, it is important to transmit significant knowledge
to actual users from various data resources. In fact, most events affect various aspects
of other areas, fields and communities. For example, in the case of the space weather, a
sensor data representing abnormality of Dst index, which is one of the sensor data on
the space weather related to Geomagnetic storm event, and news articles on
interruption of relay broadcast for XVI Olympic Winter Games are interrelated in the
context of “watching TV.” The Dst index and those news articles are individually
published from different communities. In order to understand a concept in its entirety
on user’s standpoint, a user would need to know the various interrelationships between
data in interdisciplinary fields. By only using existing search engines, however, it is
difficult to find various data resources in interdisciplinary fields. Moreover, the
interconnection will change over time. In order to manage ever-changing interrelations
among a wide variety of data repositories, it is important to realize an approach for
discovering “event-centric interrelations” of various types of data on each different
community depending on user’s standpoint.
In this paper, we present a three-layered system architecture for computing
dynamic associations of events in nature to related knowledge resources. The important
feature of our system is to realize dynamic interconnection among heterogeneous data
resources by event-driven and event-centric commuting with resolvers for uncertainties
existing among those resources. This realizes interconnection indirectly and
dynamically by semantic units for the data of various types such as text data,
multimedia data, sensor data etc. In other words, it navigates various appropriate data
including data of heterogeneous data-type and heterogeneous fields depending on user's
purpose and standpoint. In addition, it leads to effective use for the sensor data because
T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections
22](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-36-320.jpg)
![Environment Group of NICT, we are grappling with the similar issue. They require
also representing various relationships between their space weather sensor data and
other data.
Furthermore, we are working “knowledge cluster systems” for knowledge sharing,
analysis, and delivery among remote knowledge sites on a knowledge grid [3]. In this
environment, we have constructed and allocated over 400 knowledge bases to each site.
One of the important issues in this environment is how to arrange and interrelate
among these knowledge bases. We have proposed a viewpoint-dependent
interconnection method of knowledge bases by focus on concept words in each
knowledge base [4]. In this case, to arrange each knowledge base maintaining a
distributed environment, the interconnection is applied.
Therefore, in order to compute interrelation among various resources in distributed
environment, it is important to realize an interconnection mechanism depending on
some constraint for avoiding uncertainties.
2. Overview of Interconnection for Heterogeneous Content Repositories
In this section, we describe an overview of event-centric interconnection of
heterogeneous content repositories. This is a model for interconnection of
interdisciplinary data resources in distributed environment depending on some
constraint for avoiding uncertainties shown in section 1. In today’s global environment,
it is important to transmit significant knowledge to actual users from various data
resources. In order to realize this environment, it is important to interrelate among data
resources depending on some constraint for avoiding uncertainties. This framework
realizes interconnection indirectly and dynamically for the data of various types such as
text data, multimedia data, sensor data etc. That is, it helps a user to obtain various
appropriate data including data of heterogeneous data-type and heterogeneous fields
depending on user's purpose and standpoint.
The overview of an event-centric interconnection for heterogeneous contents
repositories is shown in Figure 2. Here, for realizing the framework, there are four
modules – event detection module, event projection module, correlation analysis
module and codifier module.
à Event detection module: An event detection module extracts events shown in
section 1.2 from target data depending on a condition. The condition is a kind of
constraint for avoiding uncertainty shown in section 1. The event detection
module can composite various events by setting various condition from same
target data. The diversity of data itself that is one of the uncertainties when an
event is extracted is avoided by a condition. The input of the module is target
data. It must be set in each data repository. The output of the module consists of
extracted event set. It is possible to process unitedly by making various
heterogeneous data resources an event.
à Event projection module: An event projection module projects detected event
depending on a context. We call a projected event a occurrence shown in section
1.2. The projection process corresponds to the interpretation of the event
according to the context. For example, it assumes that an event detection module
extracts a heavy rain event from article data and there are disaster ontology and
climate changing ontology. When a context is disaster, heavy rain event will be
projected in disaster ontology, and construct a new occurrence. The occurrence
T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 27](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-41-320.jpg)
![A spatiotemporal correlation analysis module is an analysis module that
specializes in the axis of time and spaces. This finds interrelationships of
the projected events (occurrences) into which the region and time hour by
hour change as phenomenon. We are developing this module based on a
moving phenomenon model [5]
Semantic correlation analysis module
A semantic correlation analysis module is an analysis module that
specializes in the semantics. This finds interrelationships of the projected
events (occurrences) depending on viewpoint. We are developing this
module based on this reference [4]
The interrelation is extracted by mutual constraint between these analysis modules.
à Codifier module
A codifier module arranges and organizes scenes extracted from a correlation
analysis management module as shown in section 2. When a user gives some
queries representing a condition, a context and a viewpoint, this module provides
appropriate scene set dynamically by RDF.
By these modules, we can obtain interrelationships between heterogeneous data by
bridging the gap between general facts and specific concepts. For example, in the case
of the space weather, a sensor data that shows abnormality of Dst index, which is one
of the sensor data on the space weather related to Geomagnetic storm event, and an
news article on interruption of relay broadcast for XVI Olympic Winter Games are
interrelated in the viewpoint of “watching TV” while they are individually published
from different communities.
7. Related Works
The relationships among concepts are predefined on the basis of a bridge concept.
Schema mappings [6] and bridge ontologies [7] are typically used for the bridge
concept. These methods are employed to predefine the universal relationships between
two different domains; however, it is quite difficult to understand these relationships in
Figure 7. An implementation for interconnection of heterogeneous contests repositories applying to space
weather data
T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections
34](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-48-320.jpg)
![most cases. As a result, conventional approaches can be employed only on a small
scale. The QOM [8] realizes semi-automatic alignment of different ontologies quickly.
However, there is no concern about contexts. That is, it is purpose to create static
whole ontologies. The feature of our method is dynamic extraction of event-centric
interrelationships depending on the content of web feeds selected by a user. The
essences of our purpose are to dynamically select, integrate and operate various
appropriate data resources depending on a context for distributed environment.
Therefore, our method is important and effective to realize interconnection of the
distributed heterogeneous data repositories.
Recently, linked data [9] that connects various resources at the instance level have
attracted attention. Especially, the Linking Open Data community project [10] tries to
connect various RDF data. The project enables us to use a large number of open
interlinked datasets as structured data. Some works extracts structured data from
Wikipedia such as DBpedia [11] and YAGO [12]. These works provide static interlinks
for RDF data. In near future, these interlinks apply to not only data but also device,
environment, resources, etc. In this sense, it is difficult to expand various interlinks
without excluding three uncertainties shown in section 1.1 because of heterogeneities
of data-type, content and utilization purpose. Our system realizes dynamic
interconnection among heterogeneous data resources by event-driven and event-centric
computing with resolvers for uncertainties existing among those resources. Therefore,
Our architecture can solve these problems.
8. Conclusion
In this paper, we presented a three-layered system architecture for computing dynamic
associations of events in nature to related knowledge resources. The important feature
of our system is to realize dynamic interconnection among heterogeneous data
resources by event-driven and event-centric commuting with resolvers for uncertainties
existing among those resources. This realizes interconnection indirectly and
dynamically by semantic units for the data of various types such as text data,
multimedia data, sensor data etc. In other words, it navigates various appropriate data
including data of heterogeneous data-type and heterogeneous fields depending on user's
purpose and standpoint.
In our current global environment, it is important to transmit significant knowledge
to actual users from various data resources. In fact, most events affect various aspects
of other areas, fields and communities. This helps a user to obtain related information
on heterogeneous data-type, contents and fields while providing a wide understanding
of the relationships between them depending on user's standpoint.
As our future study, we will extend the system to peer-to-peer environment. We
will also formulate the evaluation indexes of represented concepts and contents.
Furthermore, we will apply our method to various fields and communities.
References
[1] Space Weather Information Center, NICT, http://swc.nict.go.jp/contents/.
[2] National Space Weather Program Implementation Plan, 2nd Edition, FCM-P31-2000, Washington, DC,
July 2000.Available in PDF at http://www.ofcm.gov/nswp-ip/tableofcontents.htm.
T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 35](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-49-320.jpg)
![[3] K. Zettsu, T. Nakanishi, M. Iwazume, Y. Kidawara, Y. Kiyoki: Knowledge cluster systems for
knowledge sharing, analysis and delivery among remote sites, Information Modelling and Knowledge
Bases, vol. 19, pp. 282–289, 2008.
[4] T. Nakanishi, K. Zettsu, K. Kidawara, Y. Kiyoki: A Context Dependent Dynamic Interconnection
Method of Heterogeneous Knowledge Bases by Interrelation Management Function, In proceedings of
the 19th European-Japanese Conference on Information Modelling and Knowledge Bases, Maribor,
Slovenia, June, 2009.
[5] K.-S. Kim, K. Zettsu, K. Kidawara, Y. Kiyoki: Moving Phenomenon: Aggregation and Analysis of
Geotime-Tagged Contents on the Web, In proceedings of the 9th
international symposium on Web
Geographical Information Systems (W2GIS2009), pp.7-24, 2009.
[6] R. J. Miller, L. M. Haas, M. A. Hernandez: Schema Mapping as Query Discovery, Proc. of the 26th
International Conference on Very Large Data Bases (VLDB2000), pp. 77–88, 2000.
[7] A. H. Doan, J. Madhavan, P. Domingos, A. Halevy: Learning to Map between Ontologies on the
Semantic Web, Proc. of the 11th international conference on World Wide Web, pp. 662–673, 2002.
[8] M. Ehrig, S.Staab: QOM–Quick Ontology Mapping, In Proc. of Third International Semantic Web
Conference (ISWC 2004), pp. 683–697, Hiroshima, Japan (2004).
[9] T. Berners-Lee, Linked Data, http://www.w3.org/DesignIssues/LinkedData.html, 2006.
[10] Linking Open Data W3C SWEO Community Project,
http://esw.w3.org/topic/SweoIG/TaskForces/CommunityProjects/LinkingOpenData/.
[11] S. Auer, C. Bizer, J. Lehmann, G. Kobilarov, R. Cyganiak, Z. Ives: DBpedia: A Nucleus for a Web of
Open Data, In proceedings of the 6th International and 2nd Asian Semantic Web Conference
(ISWC2007+ASWC2007), pp.715-728, 2007.
[12] F.M. Suchanek, G. Kansneci, G Weikum: YAGO: A Core of Semantic Knowledge Unifying WordNet
and Wikipedia, In proceedings of the 16th international conference on World Wide Web, pp.697-706,
2007.
T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections
36](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-50-320.jpg)
![Partial Updates in Complex-Value
Databases
Klaus-Dieter SCHEWE a,1
and Qing WANG b,2
a
Software Competence Centre Hagenberg, Austria
b
University of Otago, Dunedin, New Zealand
Abstract. Partial updates arise when a location bound to a complex value is up-
dated in parallel. Compatibility of such partial updates to disjoint locations can be
assured by applying applicative algebras. However, due to the arbitrary nesting of
type constructors, locations of complex-value database are often defined at mul-
tiple abstraction levels and thereby non-disjoint. Thus, applicative algebras is not
as smooth as its simple definition suggests. In this paper, we investigate this prob-
lem in the context of complex-value databases, where partial updates arise natu-
rally in database transformations. We show that a more efficient solution can be ob-
tained when generalising the notion of location and thus permitting dependencies
between locations. On these grounds we develop a systematic approach to consis-
tency checking for update sets that involve partial updates.
Keywords. Abstract State Machine, partial update, complex value, applicative
algebra, database transformation
1. Introduction
According to Blass’s and Gurevich’s sequential and parallel ASM theses sequential3
and parallel algorithms are captured by sequential and general Abstract State Machines
(ASMs), respectively [3,6] (see also [4]). A decisive characteristic of ASMs is that states
are first-order structures consisting of updatable (partial) functions. Thus, in each step a
set of locations is updated to new values, where a location is defined by an n-ary function
symbol f in the (fixed) state signature of the ASM, and n values a1, . . . , an in the (fixed)
base set B of the structures defining states. That is, in a state S the function symbol f is
interpreted by a function fS : Bn
→ B, and an update of f(a1, . . . , an) to a new value
b ∈ B gives rise to fS (a1, . . . , an) = b in the successor state S
.
The progression from a state S to a successor state S
is defined by an update set Δ,
i.e. a set of updates (, b) with a location and a new value b for this location, provided
Δ is consistent, where consistency of an update set is defined by the uniqueness of new
values for all locations, i.e. whenever (, b), (, b
) ∈ Δ hold, we must have b = b
.
However, this requirement is too strict, if the base set B contains values that themselves
1E-mail: kd.schewe@scch.at
2E-mail: qing.wang@otago.ac.nz
3In Gurevich’s seminal work “parallelism” actually means unbounded parallelism, whereas algorithms with
an a priori given bound to parallelism in elementary computation steps are still considered to be sequential.
Information Modelling and Knowledge Bases XXII
A. Heimbürger et al. (Eds.)
IOS Press, 2011
© 2011 The authors and IOS Press. All rights reserved.
doi:10.3233/978-1-60750-690-4-37
37](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-51-320.jpg)
![have a complex structure. For instance, if the values for a location are tuples (A1 :
a1, . . . , Ak : ak), then updates to different attributes Ai and Aj can still be compatible.
The same applies to lists, finite sets, counters, labelled ordered trees, etc., and is therefore
of particular interest for database transformations over complex-value databases. It is
therefore desirable to distinguish between total and partial updates. For the former ones
consistency of an update set should remain unchanged, whereas for the latter ones we
should strive to find a way to guarantee compatibility and then merge partial updates to
a location in an update set into a single total update on .
The problem of partial updates in ASMs was first observed by the research group
on Foundations of Software Engineering at Microsoft Research during the development
of the executable ASM specification language AsmL [7,8]. This motivated Gurevich’s
and Tillmann’s investigation on the problem of partial updates over data types counter,
set and map [9]. An algebraic framework was established by defining particles as unary
operations over a datatype, and the parallel composition of particles as an abstraction of
order-independent sequential composition. However, this fails to address partial updates
over data types such as sequence as exemplified in [10]. This limitation led to the pro-
posal of applicative algebras as a general solution to the problem of partial updates [11].
It was shown that the problem of partial updates over sequences and labeled ordered
trees could be solved in this algebraic framework, and the approach in [9] was a special
kind of an applicative algebra.
Definition 1.1 An applicative algebra consists of elements, which comprise a trivial
element ⊥ and a non-empty set denoted by a client type τ, a monoid of total unary
operations (called particles) over the elements including a null particle λ, and a parallel
composition operation Ω, which assigns a particle ΩM to each finite multiset M of
particles, such that the following two conditions (AA1) and (AA2) are satisfied:
(AA1) f(⊥) = ⊥ for each particle f, and λ(x) = ⊥ for every element x.
(AA2) Ω{
{f}
} = f, Ω(M {
{id}
}) = ΩM, and Ω(M {
{λ}
}) = λ.
A multiset M of particles is called consistent iff ΩM = λ.
When applying applicative algebras to the problem of partial updates each partial
update (, b) has to be interpreted as a partical applied to the content of in state S
(denoted by valS()) and all these particles form a multiset M that is aggregated to ΩM
such that valS () = ΩM(valS()) holds, provided M is consistent.
In this paper, we investigate the partial update problem in the context of complex-
value databases. In database transformations, bounded parallelism is intrinsic and com-
plex data structures form the core of each data model. Thus, the problem of partial
updates arises naturally. Several examples of partial update problems encountered in
complex-value database are provided in Section 2.
Furthermore, in Section 2, we discuss the reasons why using applicative algebras
is not as smooth as the simple definition above suggests. One of important assumptions
of applicative algebra is that locations of partial updates must be disjoint. However, it is
common in data models to permit the arbitrary nesting of complex-value constructors.
Consequently, we need particles for each position in a complex value, and each nested
structure requires its own parallel composition operation. It means that we have to deal
with the theoretical possibility of infinitely many applicative algebras, which requires a
K.-D. Schewe and Q. Wang / Partial Updates in Complex-Value Databases
38](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-52-320.jpg)
![mechanism for the construction of such algebras out of algebras for parts of the type of
every object in a complex-value database. This leads to the question of how to efficiently
check consistency for sets of partial updates.
In view of these problems we propose an alternative solution to the problem of par-
tial updates. The preliminaries such as the definition of partial locations, partial updates,
and different kinds of dependencies among partial locations are handled in Section 3. We
relax the disjointness assumption on the notion of location in order to reflect a natural
and flexible computing environment for database computations. While in principle the
prime locations bound to complex values are not independent from each other, we may
consider each position within a complex value as a sublocation, which for simplicity of
terminology we prefer to call also location. Then a partial update to a location is in fact
a (partial) update to a sublocation.
In doing so, we can transform the problems of consistency checking and parallel
composition into two stages: normalisation of shared updates and integration of total
updates, which are discussed in Section 4 and Section 5, correspondingly. The first stage
deals with compatibility of operators in shared updates and the second one deals with
compatibility of clusters of exclusive updates.
The work in this paper is part of our research on formal foundations of database
transformations. Taking an approach analogous to the ASM thesis we demonstrated that
all database transformations are captured by a variant of Abstract State Machines [13].
Decisive for this work is the exploitation of meta-finite states [5] in order to capture the
intrinsic finiteness of databases, the explicit use of background structures [2] to capture
the requirements of data models, and the handling of genericity [1]. For XML database
transformations the requirements for tree-based backgrounds were made explicit in [12],
and a more convenient machine model called XML machines was developed permitting
the use of monadic second-order logic. On these grounds we developed a logic to reason
about database transformations [14].
2. Motivation
We begin with modifications on tuples in a relation since tuples represent a common
view for locations in the relational model. As will be revealed in the following example,
parallel manipulations on distinct attributes of a tuple are prohibited if only tuples are
permissible locations in a state.
Example 2.1 Let S be a state containing a nested relation schema R = {A1 : {A11 :
D11, A12 : D22}, A2 : D2, A3 : D3} and a nested relation I(R) over R as shown in
Figure 1 where oi (i = 1, 3) are tuple identifiers in I(R) and oij (j = 1, 2) are tuple
identifers in the relations in the attribute A1 of tuples oi. Suppose that the following two
rules execute in parallel, modifying values of attributes A2 and A3 of the same tuple.
forall x, y, z with R(x, y, z) ∧ y = b3
do
par
R(x, y, z) := false
R(x, y, c2) := true
par
enddo
forall x, y, z with R(x, y, z) ∧ y = b3
do
par
R(x, y, z) := false
R(x, b, z) := true
par
enddo
K.-D. Schewe and Q. Wang / Partial Updates in Complex-Value Databases 39](https://image.slidesharecdn.com/1118203-250606104121-70eaad1a/85/Information-Modelling-And-Knowledge-Bases-Xxii-A-Heimbrrger-53-320.jpg)
Information Modelling And Knowledge Bases Xxii A Heimbrrger
- 1. Information Modelling And Knowledge Bases Xxii A Heimbrrger download https://ebookbell.com/product/information-modelling-and- knowledge-bases-xxii-a-heimbrrger-2236406 Explore and download more ebooks at ebookbell.com
- 2. Here are some recommended products that we believe you will be interested in. You can click the link to download. Information Modelling And Knowledge Bases Xxxi Frontiers In Artificial Intelligence And Applications Ajantha Dahanayake Editor https://ebookbell.com/product/information-modelling-and-knowledge- bases-xxxi-frontiers-in-artificial-intelligence-and-applications- ajantha-dahanayake-editor-36679114 Information Modelling And Knowledge Bases Xxxii M Tropmannfrick https://ebookbell.com/product/information-modelling-and-knowledge- bases-xxxii-m-tropmannfrick-44851488 Information Modelling And Knowledge Bases Xviii M Duza H Jaakkola https://ebookbell.com/product/information-modelling-and-knowledge- bases-xviii-m-duza-h-jaakkola-989272 Information Modelling And Knowledge Bases Xvii J Henno H Jaakkola Y Kiyoki https://ebookbell.com/product/information-modelling-and-knowledge- bases-xvii-j-henno-h-jaakkola-y-kiyoki-992660
- 3. Information Modelling And Knowledge Bases Xiii Hannu Kangassalo https://ebookbell.com/product/information-modelling-and-knowledge- bases-xiii-hannu-kangassalo-1625068 Information Modelling And Knowledge Bases Xix H Jaakkola Y Kiyoki https://ebookbell.com/product/information-modelling-and-knowledge- bases-xix-h-jaakkola-y-kiyoki-2139344 Information Modelling And Knowledge Bases Xiv Hannu Jaakkola https://ebookbell.com/product/information-modelling-and-knowledge- bases-xiv-hannu-jaakkola-2243514 Information Modelling And Knowledge Bases Xxv T Tokuda Y Kiyoki https://ebookbell.com/product/information-modelling-and-knowledge- bases-xxv-t-tokuda-y-kiyoki-5331022 Information Modelling And Knowledge Bases Xv Yasushi Kiyoki Yasushi Kiyoki https://ebookbell.com/product/information-modelling-and-knowledge- bases-xv-yasushi-kiyoki-yasushi-kiyoki-992018
- 5. INFORMATION MODELLING AND KNOWLEDGE BASES XXII
- 6. Frontiers in Artificial Intelligence and Applications FAIA covers all aspects of theoretical and applied artificial intelligence research in the form of monographs, doctoral dissertations, textbooks, handbooks and proceedings volumes. The FAIA series contains several sub-series, including “Information Modelling and Knowledge Bases” and “Knowledge-Based Intelligent Engineering Systems”. It also includes the biennial ECAI, the European Conference on Artificial Intelligence, proceedings volumes, and other ECCAI – the European Coordinating Committee on Artificial Intelligence – sponsored publications. An editorial panel of internationally well-known scholars is appointed to provide a high quality selection. Series Editors: J. Breuker, N. Guarino, J.N. Kok, J. Liu, R. López de Mántaras, R. Mizoguchi, M. Musen, S.K. Pal and N. Zhong Volume 225 Recently published in this series Vol. 224. J. Barzdins and M. Kirikova (Eds.), Databases and Information Systems VI – Selected Papers from the Ninth International Baltic Conference, DB&IS 2010 Vol. 223. R.G.F. Winkels (Ed.), Legal Knowledge and Information Systems – JURIX 2010: The Twenty-Third Annual Conference Vol. 222. T. Ågotnes (Ed.), STAIRS 2010 – Proceedings of the Fifth Starting AI Researchers’ Symposium Vol. 221. A.V. Samsonovich, K.R. Jóhannsdóttir, A. Chella and B. Goertzel (Eds.), Biologically Inspired Cognitive Architectures 2010 – Proceedings of the First Annual Meeting of the BICA Society Vol. 220. R. Alquézar, A. Moreno and J. Aguilar (Eds.), Artificial Intelligence Research and Development – Proceedings of the 13th International Conference of the Catalan Association for Artificial Intelligence Vol. 219. I. Skadiņa and A. Vasiļjevs (Eds.), Human Language Technologies – The Baltic Perspective – Proceedings of the Fourth Conference Baltic HLT 2010 Vol. 218. C. Soares and R. Ghani (Eds.), Data Mining for Business Applications Vol. 217. H. Fujita (Ed.), New Trends in Software Methodologies, Tools and Techniques – Proceedings of the 9th SoMeT_10 Vol. 216. P. Baroni, F. Cerutti, M. Giacomin and G.R. Simari (Eds.), Computational Models of Argument – Proceedings of COMMA 2010 Vol. 215. H. Coelho, R. Studer and M. Wooldridge (Eds.), ECAI 2010 – 19th European Conference on Artificial Intelligence ISSN 0922-6389 (print) ISSN 1879-8314 (online)
- 7. Information Modelling and Knowledge Bases XXII Edited by Anneli Heimbürger University of Jyväskylä, Finland Yasushi Kiyoki Keio University, Japan Takehiro Tokuda Tokyo Institute of Technology, Japan Hannu Jaakkola Tampere University of Technology, Finland and Naofumi Yoshida Komazawa University, Japan Amsterdam • Berlin • Tokyo • Washington, DC
- 8. © 2011 The authors and IOS Press. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without prior written permission from the publisher. ISBN 978-1-60750-689-8 (print) ISBN 978-1-60750-690-4 (online) Library of Congress Control Number: 2010942038 Publisher IOS Press BV Nieuwe Hemweg 6B 1013 BG Amsterdam Netherlands fax: +31 20 687 0019 e-mail: order@iospress.nl Distributor in the USA and Canada IOS Press, Inc. 4502 Rachael Manor Drive Fairfax, VA 22032 USA fax: +1 703 323 3668 e-mail: iosbooks@iospress.com LEGAL NOTICE The publisher is not responsible for the use which might be made of the following information. PRINTED IN THE NETHERLANDS
- 9. Preface In recent decades information modeling and knowledge bases have become hot topics, not only in academic communities related to information systems and computer science but also in the business area where information technology is applied. The 20th Euro- pean-Japanese Conference on Information Modeling and Knowledge Bases (EJC2010) continues the series of events that originally started as a co-operation initiative between Japan and Finland, back in the second half of the 1980’s. Later (1991) the geographical scope of these conferences expanded to cover the whole of Europe and other countries as well. The EJC conferences constitute a worldwide research forum for the exchange of scientific results and experiences achieved in computer science and other related disci- plines using innovative methods and progressive approaches. In this way a platform has been established drawing together both researchers and practitioners who deal with information modelling and knowledge bases. The main topics of EJC conferences tar- get the variety of themes in the domain of information modeling: conceptual analysis, the design and specification of information systems, multimedia information modelling, multimedia systems, ontology, software engineering, knowledge and process manage- ment, knowledge bases, cross-cultural communication and context modelling. We also aim at applying new progressive theories. To this end much attention is also paid to theoretical disciplines including cognitive science, artificial intelligence, logic, linguis- tics and analytical philosophy. In order to achieve the targets of the EJC, an international program committee se- lected 15 full papers and 10 short papers in a rigorous reviewing process from 34 sub- missions. The selected papers cover many areas of information modelling, namely the theory of concepts, database semantics, knowledge representation, software engineer- ing, WWW information management, context-based information retrieval, ontological technology, image databases, temporal and spatial databases, document data manage- ment, process management, cultural modelling and many others. The conference could not be a success without a lot of effort on the part of many people and organizations. In the program committee, 29 reputable researchers devoted a lot of energy to the review process, selecting the best papers and creating the EJC2010 program, and we are very grateful to them. Professor Yasushi Kiyoki and Professor Takehiro Tokuda acted as co-chairs of the program committee while Senior Researcher, Dr. Anneli Heimbürger, and her team took care of the conference venue and local arrangements. Professor Hannu Jaakkola acted as the general organizing chair and Ms. Ulla Nevanranta as conference secretary for the general organizational matters necessary for running the annual conference series. Dr. Naofumi Yoshida and his Pro- gram Coordination Team managed the review process and the conference program. We also gratefully appreciate the efforts of all our supporters, especially the Department of Mathematical Information Technology at the University of Jyväskylä (Finland), for supporting this annual event and the 20th jubilee year of EJC. Information Modelling and Knowledge Bases XXII A. Heimbürger et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. v
- 10. We believe that the conference was productive and fruitful in the advance of re- search and application of information modelling and knowledge bases. This book fea- tures papers edited as a result of the presentation and discussion at the conference. The Editors Anneli Heimbürger, University of Jyväskylä, Finland Yasushi Kiyoki, Keio University, Japan Takehiro Tokuda, Tokyo Institute of Technology, Japan Hannu Jaakkola, Tampere University of Technology (Pori), Finland Naofumi Yoshida, Komazawa University, Japan vi
- 11. Conference Committee General Programme Chair Hannu Kangassalo, University of Tampere, Finland Co-Chairs Yasushi Kiyoki, Keio University, Japan Takehiro Tokuda, Tokyo Institute of Technology, Japan Members Maria Bielikova, Slovak University of Technology in Bratislava, Slovakia Boštjan Brumen, University of Maribor, Slovenia Pierre-Jean Charrel, University of Toulouse and IRIT, France Xing Chen, Kanagawa Institute of Technology, Japan Alfredo Cuzzocrea, ICAR Institute and University of Calabria, Italy Marie Duží, VSB-Technical University Ostrava, Czech Republic Jørgen Fischer Nilsson, Techinical University of Denmark, Denmark Hele-Mai Haav, Institute of Cybernetics at Tallinn University of Technology, Estonia Roland Hausser, Erlangen University, Germany Anneli Heimbürger, University of Jyväskylä, Finland Jaak Henno, Tallinn University of Technology, Estonia Yoshihide Hosokawa, Gunma University, Japan Hannu Jaakkola, Tampere University of Technology, Pori, Finland Ahto Kalja, Tallinn University of Technology, Estonia Eiji Kawaguchi, Kyushu Institute of Technology, Japan Mauri Leppänen, University of Jyväskylä, Finland Sebastian Link, Victoria University of Wellington, New Zealand Tommi Mikkonen, Tampere University of Technology, Finland Jari Palomäki, Tampere University of Technology, Pori, Finland Hideyasu Sasaki, Ritsumeikan University, Japan Tetsuya Suzuki, Shibaura Institute of Technology, Japan Bernhard Thalheim, Kiel University, Germany Peter Vojtáš, Charles University Pragu, Czech Republic Yoshimichi Watanabe, University of Yamanashi, Japan Naofumi Yoshida, Komazawa University, Japan Koji Zettsu, NICT, Japan General Organizing Chair Hannu Jaakkola, Tampere University of Technology, Pori, Finland vii
- 12. Organizing Committee Anneli Heimbürger, University of Jyväskylä, Finland Xing Chen, Kanagawa Institute of Technology, Japan Ulla Nevanranta, Tampere University of Technology, Pori, Finland Program Coordination Team Naofumi Yoshida, Komazawa University, Japan Xing Chen, Kanagawa Institute of Technology, Japan Anneli Heimbürger, University of Jyväskylä, Finland Jari Palomäki, Tampere University of Technology, Pori, Finland Teppo Räisänen, University of Oulu, Finland Daniela Ďuráková, Technical University of Ostrava, Czech Republic Akio Takashima, Hokkaido University, Japan Tomoya Noro, Tokyo Institute of Technology, Japan Turkka Näppilä, University of Tampere, Finland Jukka Aaltonen, University of Lapland, Finland External Reviewers Thomas Proisl Besim Kabashi viii
- 13. Contents Preface v Anneli Heimbürger, Yasushi Kiyoki, Takehiro Tokuda, Hannu Jaakkola and Naofumi Yoshida Ontology As a Logic of Intensions 1 Marie Duží, Martina Číhalová and Marek Menšík A Three-Layered Architecture for Event-Centric Interconnections Among Heterogeneous Data Repositories and Its Application to Space Weather 21 Takafumi Nakanishi, Hidenori Homma, Kyoung-Sook Kim, Koji Zettsu, Yutaka Kidawara and Yasushi Kiyoki Partial Updates in Complex-Value Databases 37 Klaus-Dieter Schewe and Qing Wang Inferencing in Database Semantics 57 Roland Hausser Modelling a Query Space Using Associations 77 Mika Timonen, Paula Silvonen and Melissa Kasari Architecture-Driven Modelling Methodologies 97 Hannu Jaakkola and Bernhard Thalheim An Emotion-Oriented Image Search System with Cluster Based Similarity Measurement Using Pillar-Kmeans Algorithm 117 Ali Ridho Barakbah and Yasushi Kiyoki The Quadrupel – A Model for Automating Intermediary Selection in Supply Chain Management 137 Remy Flatt, Markus Kirchberg and Sebastian Link A Simple Model of Negotiation for Cooperative Updates on Database Schema Components 154 Stephen J. Hegner A Description-Based Approach to Mashup of Web Applications, Web Services and Mobile Phone Applications 174 Prach Chaisatien and Takehiro Tokuda A Formal Presentation of the Process-Ontological Model 194 Jari Palomäki and Harri Keto Performance Forecasting for Performance Critical Huge Databases 206 Bernhard Thalheim and Marina Tropmann Specification of Games 226 Jaak Henno ix
- 14. Bridging Topics for Story Generation 247 Makoto Sato, Mina Akaishi and Koichi Hori A Combined Image-Query Creation Method for Expressing User’s Intentions with Shape and Color Features in Multiple Digital Images 258 Yasuhiro Hayashi, Yasushi Kiyoki and Xing Chen Towards Context Modelling and Reasoning in a Ubiquitous Campus 278 Ekaterina Gilman, Xiang Su and Jukka Riekki A Phenomena-of-Interest Approach for the Interconnection of Sensor Data and Spatiotemporal Web Contents 288 Kyoung-Sook Kim, Takafumi Nakanishi, Hidenori Homma, Koji Zettsu, Yutaka Kidawara and Yasushi Kiyoki Modelling Contexts in Cross-Cultural Communication Environments 301 Anneli Heimbürger, Miika Nurminen, Teijo Venäläinen and Suna Kinnunen Towards Semantic Modelling of Cultural Historical Data 312 Ari Häyrinen A Collaboration Model for Global Multicultural Software Development 321 Taavi Ylikotila and Petri Linna A Culture-Dependent Metadata Creation Method for Color-Based Impression Extraction with Cultural Color Spaces 333 Totok Suhardijanto, Kiyoki Yasushi and Ali Ridho Barakbah R-Web: A Role Accessibility Definition Based Web Application Generation 344 Yusuke Nishimura, Kosuke Maebara, Tomoya Noro and Takehiro Tokuda NULL ‘Value’ Algebras and Logics 354 Bernhard Thalheim and Klaus-Dieter Schewe Ontology Representation and Inference Based on State Controlled Coloured Petri Nets 368 Ke Wang, James N.K. Liu and Wei-min Ma The Discourse Tool: A Support Environment for Collaborative Modeling Efforts 378 Denis Kozlov, Tore Hoel, Mirja Pulkkinen and Jan M. Pawlowski On Context Modelling in Systems and Applications Development 396 Anneli Heimbürger, Yasushi Kiyoki, Tommi Kärkkäinen, Ekaterina Gilman, Kyoung-Sook Kim and Naofumi Yoshida Future Directions of Knowledge Systems Environments for Web 3.0 413 Koji Zettsu, Bernhard Thalheim, Yutaka Kidawara, Elina Karttunen and Hannu Jaakkola Subject Index 447 Author Index 449 x
- 15. Ontology as a Logic of Intensions Marie DUŽÍa,1 , Martina ÍHALOVÁa , Marek MENŠÍKa,b a VSB-Technical University Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic b Institute of Computer Science, FPF, Silesian University in Opava, Bezruovo nám. 13, 746 01 Opava, Czech Republic m.tina.cihal@gmail.com, marie.duzi@vsb.cz, mensikm@gmail.com Abstract. We view the content of ontology via a logic of intensions. This is due to the fact that particular intensions like properties, roles, attributes and propositions can stand in mutual necessary relations which should be registered in the ontology of a given domain, unlike some contingent facts. The latter are a subject of updates and are stored in a knowledge-base state. Thus we examine (higher-order) properties of intensions like being necessarily reflexive, irreflexive, symmetric, anti-symmetric, transitive, etc., mutual relations between intensions like being incompatible, being a requisite, being complementary, and so like. We also define two kinds of entailment relation between propositions, viz. mere entailment and presupposition. Finally, we show that higher-order properties of propositions trigger necessary integrity constraints that should also be included in the ontology. As the logic of intensions we vote for Transparent Intensional Logic (TIL), because TIL framework is smoothly applicable to all three kinds of context, viz. extensional context of individuals, numbers and functions-in-extension (mappings), intensional context of properties, roles, attributes and propositions, and finally hyper-intensional context of procedures producing intensional and extensional entities as their products. Keywords. Ontology, intension, hyperintension, Transparent Intensional Logic, integrity constraint. Introduction In informatics, the term ‘ontology’ has been borrowed from philosophy, where ontology is a systematic account of existence. In most general, what exists is that what can be represented. Thus in recent Artificial Intelligence and information systems a formal ontology is an explicit and systematic conceptualization of a domain of interest. Given a domain, ontological analysis should clarify the structure of knowledge on what exists in the domain. A formal ontology is, or should be, a stable heart of an information system that makes knowledge sharing, reuse and reasoning possible. As J. Sowa says in [14, p. 51], “logic itself has no vocabulary for describing the things that exist. Ontology fills that gap: it is the study of existence, of all the kinds of entities abstract and concrete that make up the world”. Current languages and tools applicable in the area of an ontology design focus in particular on the form of ontological representation rather than what a semantic content of ontology should be. Of course, a unified syntax is useful, but the problems of syntax 1 Corresponding Author. Information Modelling and Knowledge Bases XXII A. Heimbürger et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-690-4-1 1
- 16. are almost trivial compared to the problems of developing a common semantics for any domain. In this paper we focus on ontology content rather than a form. We concentrate on describing concepts necessary for the specification of relations between higher-order entities like properties, roles/offices, attributes and propositions, which are all modelled as PWS (possible-world semantics) intensions, i.e. functions with the set of possible worlds as their domain. To this end we apply the procedural semantics of Transparent Intensional Logic (TIL), which provides a universal framework applicable smoothly in all three kinds of context, namely extensional context of individuals, numbers and functions-in-extension, intensional context of PWS-intensions and finally hyper- intensional context of concepts viewed as abstract procedures producing extensional as well as intensional entities as their products.2 The paper is organised as follows. Ontology content and languages for ontology specification are introduced in Section 1. Here we also provide a brief introduction to Transparent Intensional Logic, the tool we are going to apply throughout the paper. In Section 2 we introduce our logic of intensions, in particular the logic of requisites. Section 3 tackles the phenomenon of presupposition and compares it with mere entailment. Finally, concluding Section 4 outlines further research. 1. Ontology content and knowledge representation Knowledge representation is a multidisciplinary discipline that applies theories and tools of logic and ontology. It comprises both knowledge base and ontology design. Yet there is a substantial distinction between the former and the latter. Whereas the content of a knowledge base state consists in particular of contingent values of (empirical) attributes, the ontology content comprises in particular the taxonomy of entities that should not depend on contingent facts. Thus, for instance in Description Logic (DL) we distinguish between definitional and incidental part, the former containing concepts of attributes rather than their values. The main reason for building knowledge-based systems comprising ontologies can be characterized as making hidden knowledge explicit and logically tractable. To this end it is desirable to apply an expressive semantic framework in order that all the semantically salient features of knowledge specification can be adequately represented so that reasoning based on this representation is logically adequate and does not yield paradoxes. In general, current ontology languages are mostly based on the 1st -order predicate logic (FOL). Though FOL has become stenography of mathematics, it is not expressive enough when applied in other areas such as ontology specification. The obvious shortcoming of the FOL approach is this: in FOL we must treat higher-order intensions and hyper-intensions as elements of a flat universe, due to which knowledge representation is not comprehensible enough. Moreover, when representing knowledge in FOL, the well-known problem of the paradox of omniscience is almost inevitable. For applications where FOL is not adequate, it would be desirable to extend the framework to a higher-order logic (HOL). A general objection against using HOL logic is its computational intractability. However, HOL formulas are relatively well understood, and reasoning systems for HOLs do already exist, e.g., HOL [6] and Isabel [13]. 2 Recent most up-to-date results and applications of TIL can be found in [5]. M. Duží et al. / Ontology As a Logic of Intensions 2
- 17. 1.1. Standard ontological languages There are a number of languages which have been developed for knowledge representation. They provide tools for knowledge-base specification and deductive reasoning using the specified knowledge. Of these, perhaps the best known and broadly used logical calculi are F-logic and Description Logic (DL) in their various variants.3 The F-logic arose from the practice of frame systems. Thus it can be viewed as a hierarchy of classes of elements which are furnished with attributes, accompanied by inference rules. The DL-philosophy is different; it makes use of the notion of a logical theory defined as a set of special axioms built over the first-order predicate logic calculus. Particular classes and their mutual relations are defined by logical formulas. Thus in DL the class hierarchy typical for frame systems is not directly specified. Rather, it is dynamically derived using logical definitions (class descriptions). Though the existing ontology languages have been enriched by a few constructs exceeding the power of FOL, these additional constructs are usually not well defined and understood. Moreover, particular languages are neither syntactically nor semantically compatible. The W3C efforts at standardization resulted in accepting the Resource Description Framework (RDF) language as the Web ontological recommendation. However, this situation is far from satisfactory. Quoting from Horrocks and Schneider [8]: “The thesis of representation underlying RDF and RDFS is particularly troublesome in this regard, as it has several unusual aspects, both semantic and syntactic. A more-standard thesis of representation would result in the ability to reuse existing results and tools in the Semantic Web.” RDF includes three basic elements. Resources are anything with an URI address. Properties specify attributes and/or (binary) relations between resources and an object used to describe resources. Statements of the form ‘subject, predicate, object’ associate a resource and a specific value of its property. RDF has unusual aspects that make its use as the foundation of representation in the area of ontology building and Semantic Web difficult at best. In particular, RDF has a very limited collection of syntactic constructs, and these are treated in a very uniform manner in the semantics of RDF. The RDF syntax consists of the so-called triples – subject, predicate and object, where only binary predicates are allowed. This causes serious problems concerning compatibility with more expressive languages. The RDF thesis requires that no other syntactic constructs than the RDF triples are to be used and that the uniform semantic treatment of syntactic constructs cannot be changed only augmented. In RDFS we can specify classes and properties of individuals, constraints on properties, and the relation of subsumption (subclass, subproperty). It is not possible, for instance, to specify properties of properties, e.g., that the relation (property) is functional or transitive. Neither it is possible to define classes by means of properties of individuals that belong to the class. The RDF like languages originally did not have a model theoretic semantics, which led to many discrepancies. As stated above, RDF(S) is recommended by W3C, and its usage is world spread. The question is whether it is a good decision. A classical FOL approach would be better, or even its standard extension to HOL would be more suitable for ontologies. Formalisation in HOL is much more natural and comprehensive, the universe of discourse is not a flat set of ‘individuals’; rather, properties and relations can be naturally talked about as well, which is much more apt for representation of ontologies. 3 For details on Description Logic and F-logic see, for instance, [1] and [11], respectively. M. Duží et al. / Ontology As a Logic of Intensions 3
- 18. Recognition of the limitations of RDFS led to the development of ontology languages such as OIL, DAML-ONT and DAML+OIL, which resulted into the OWL. OWL has been developed as an extension of RDFS. OWL (like DAML+OIL) uses the same syntax as RDF (and RDFS) to represent ontologies, the two languages are syntactically compatible. However, the semantic layering of the two languages is more problematical. The difficulty stems from the fact that OWL (like DAML+OIL) is largely based on DL, the semantics of which would normally be given by a classical first-order model theory in which individuals are interpreted as elements of some domain (a set), classes are interpreted as subsets of the domain and properties are interpreted as binary relations on the domain. The semantics of RDFS, on the other hand, are given by a non-standard model theory, where individuals, classes and properties are all elements in the domain. Properties are further interpreted as having extensions which are binary relations on the domain, and class extensions are only implicitly defined by the extension of the rdf:type property. Moreover, RDFS supports reflection on its own syntax: interpretation of classes and properties can be extended by statements in the language. Thus language layering is much more complex, because different layers subscribe to these two different approaches. A bit more sophisticated approach is provided by the OWL (Ontology Web Language) that is also recommended by W3C, which is based on DL framework. In DL we talk about individuals that are elements of a universe domain. The individuals are members of subclasses of the domain, and can be related to other individuals (or data values) by means of properties (n-ary relations are called properties in Web ontologies, for they are decomposed into n properties). The universe of discourse is divided into two disjoint sorts: the object domain of individuals and the data value domain of numbers. Thus the interpretation function assigns elements of the object domain to individual constants, elements of data value domain to value constants, and subclasses of the data domain to data types. Further, object and data predicates are distinguished, the former being interpreted as a subset of the Cartesian product of object domain, the latter a subset of the Cartesian product of value domain. DL is rather rich, though being an FOL language. It makes it possible to distinguish intensional knowledge (knowledge on the analytically necessary relations between concepts) and extensional knowledge (of contingent facts). To this end DL knowledge base includes the so-called T-boxes (terminology or taxonomy) and A-boxes (contingent attributes of objects). T-box contains verbal definitions, i.e., a new concept is defined composing known concepts. For instance, a woman can be defined: WOMAN = PERSON SEX- FEMALE, and a mother: MOTHER = WOMAN child(HASchild). Thus the fact that, e.g., mother is a woman is analytic (necessary) truth. In T-boxes there are also specifications of necessary properties of concepts and relations between concepts: the property satisfiability corresponds to a nonempty concept, the relation of subsumption (intensionally contained concepts), equivalence and disjointness (incompatibility). Thus, e.g., that a bachelor is not married is analytically true proposition. On the other hand, the fact that, e.g., Mr. Jones is a bachelor is a contingent unnecessary fact. Such contingent properties (attributes) of objects are recorded in A-boxes. The third group of ontology languages lies somewhere between the FOL framework and RDFS. This group comprises SKIF and Common Logic [7]. The SKIF syntax is compatible with functional language LISP, but in principle it is an FOL syntax. These languages also have a non standard model theory, with predicates being interpreted as individuals, i.e., elements of a domain. Classes are however treated as subsets of the domain, and their redefinition in the language syntax is not allowed. M. Duží et al. / Ontology As a Logic of Intensions 4
- 19. Based on common logic, the SKIF language accommodates some higher-order constructs. The SKIF languages are syntactically compatible with LISP, i.e., the FOL syntax is extended with the possibility to mention properties and use variables ranging over properties. For instance, we can specify that John and Peter have a common property: p.p(John) p(Peter). The property they have in common can be, e.g., that they both love their wives. We can also specify that a property P is true of John, and the P has the property Q: P(John) Q(P). If P is being honest and Q is being eligible, the sentence can be read as that John is honest, which is eligible. The interpretation structure is a triple ¢D, ext, V², where D is the universe, V is the function that maps predicates, variables and constants to the elements of D, and ext is the function that maps D into sets of n-tuples of elements of D. SKIF does not reduce the arity of predicates. To our best knowledge, the only ontology language supporting inferences at this level is a Semantic Web Rule Language (SWRL) combining OWL and RuleML [9]. According to the OWL (Web Ontology Language) overview [19], OWL is intended to be used when information contained in documents needs to be processed by applications, as opposed to situations where the contents only need to be presented to humans. OWL can be used to represent the meaning of terms in vocabularies and relationships between those terms. OWL has been designed on the top of XML, XLink, RDF and RDFS in order to provide more facilities for expressing meaning and semantics to represent machine interpretable content on the Web. Summarising, well-defined ontology should serve at least these goals: (1) universal library to be accessed and used by humans in a variety of information use contexts, (2) the backdrop work of computational agents carrying out activities on behalf of humans, and (3) a method for integrating knowledge bases and databases to perform tasks for humans. Current ontology languages, however, are far from meeting these goals, and their expressive power does not enable computational agents to make use of an adequate inference machine. Still worse, from a logical-semantic point of view these languages suffer the following shortcomings. None of them (perhaps with an exception of languages based on DL) makes it possible to express modalities (what is necessary and what is contingent), to distinguish three kinds of context, viz. extensional level of objects like individuals, numbers, functions (-in-extension), intensional level of properties, propositions, offices and roles, and finally hyperintensional level of concepts (i.e. algorithmically structured procedures). Concepts of n-ary relations are unreasonably modelled by properties. True, each n-ary relation can be expressed by n unary relations (properties) but such a representation is misleading and incomprehensible. Ontology language should be, however, universal, highly expressive, with transparent semantics and meaning driven axiomatisation. For these reasons we vote for an expressive system of Transparent Intensional Logic (TIL). From the formal point of view, TIL is a hyper-intensional, partial, typed O-calculus. Hyperintensional, because we apply top-down approach to semantics, from hyper-intensional (conceptual) level of procedures, via intensional down to extensional level of abstraction. Basic semantic construct is an abstract procedure known as TIL construction. Since TIL has been referred to in numerous EJC papers, in the next paragraph we only briefly recapitulate basic principles of TIL. For the most up-to-date exposition, see [5] and also [10]. M. Duží et al. / Ontology As a Logic of Intensions 5
- 20. 1.2. A brief introduction to TIL TIL is an overarching semantic theory for all sorts of discourse, whether colloquial, scientific, mathematical or logical. The theory is a procedural one, according to which sense is an abstract, pre-linguistic procedure detailing what operations to apply to what procedural constituents to arrive at the product (if any) of the procedure. Such procedures are rigorously defined as TIL constructions. The semantics is entirely anti- contextual and compositional and it is, to the best of our knowledge, the only one that deals with all kinds of context in a uniform way. Thus the sense of a sentence is an algorithmically structured construction of the proposition denoted by the sentence. The denoted proposition is a flat, or unstructured, mapping with domain in a logical space of possible worlds. Our motive for working ‘top-down’ has to do with anti- contextualism: any given unambiguous term or expression (even one involving indexicals or anaphoric pronouns) expresses the same construction as its sense whatever sort of context the term or expression is embedded within. And the meaning of an expression determines the respective denoted entity (if any), but not vice versa. The denoted entities are (possibly 0-ary) functions understood as set-theoretical mappings. Thus we strictly distinguish between a procedure (construction) and its product (here, a constructed function), and between a function and its value. Intuitively, construction C is a procedure (a generalised algorithm). Constructions are structured in the following way. Each construction C consists of sub-instructions (constituents), each of which needs to be executed when executing C. Thus a specification of a construction is a specification of an instruction on how to proceed in order to obtain the output entity given some input entities. There are two kinds of constructions, atomic and compound (molecular). Atomic constructions (Variables and Trivializations) do not contain any other constituent but themselves; they specify objects (of any type) on which compound constructions operate. The variables x, y, p, q, …, construct objects dependently on a valuation; they v-construct. The Trivialisation of an object X (of any type, even a construction), in symbols 0 X, constructs simply X without the mediation of any other construction. Compound constructions, which consist of other constituents as well, are Composition and Closure. Composition [F A1…An] is the operation of functional application. It v- constructs the value of the function f (valuation-, or v-, -constructed by F) at a tuple argument A (v-constructed by A1, …, An), if the function f is defined at A, otherwise the Composition is v-improper, i.e., it fails to v-construct anything.4 Closure [Ox1…xn X] spells out the instruction to v-construct a function by abstracting over the values of the variables x1,…,xn in the ordinary manner of the O-calculi. Finally, higher-order constructions can be used twice over as constituents of composite constructions. This is achieved by a fifth construction called Double Execution, 2 X, that behaves as follows: If X v-constructs a construction X’, and X’ v-constructs an entity Y, then 2 X v-constructs Y; otherwise 2 X is v-improper, failing as it does to v-construct anything. TIL constructions, as well as the entities they construct, all receive a type. The formal ontology of TIL is bi-dimensional; one dimension is made up of constructions, the other dimension encompasses non-constructions. On the ground level of the type hierarchy, there are non-constructional entities unstructured from the algorithmic point of view belonging to a type of order 1. Given a so-called epistemic (or objectual) base 4 As mentioned above, we treat functions as partial mappings, i.e., set-theoretical objects, unlike the constructions of functions. M. Duží et al. / Ontology As a Logic of Intensions 6
- 21. of atomic types (R-truth values, L-individuals, W-time moments / real numbers, Z- possible worlds), the induction rule for forming functional types is applied: where D, E1,…,En are types of order 1, the set of partial mappings from E1 u…u En to D, denoted ‘(D E1…En)’, is a type of order 1 as well.5 Constructions that construct entities of order 1 are constructions of order 1. They belong to a type of order 2, denoted ‘*1’. The type *1 together with atomic types of order 1 serves as a base for the induction rule: any collection of partial mappings, type (D E1…En), involving *1 in their domain or range is a type of order 2. Constructions belonging to a type *2 that identify entities of order 1 or 2, and partial mappings involving such constructions, belong to a type of order 3. And so on ad infinitum. The sense of an empirical expression is a hyperintension that is a construction that produces a (possible world) D-intension, where D-intensions are members of type (DZ), i.e., functions from possible worlds to an arbitrary type D. On the other hand, D- extensions are members of a type D, where D is not equal to (EZ) for any E, i.e., extensions are functions whose domain is not the set of possible worlds. Intensions are frequently functions of a type ((DW)Z), i.e., functions from possible worlds to chronologies of the type D (in symbols: DWZ), where a chronology is a function of type (DW). Some important kinds of intensions are: Propositions, type RWZ. They are denoted by empirical sentences. Properties of members of a type D, or simply D-properties, type (RD)WZ.6 General terms, some substantives, intransitive verbs (‘student’, ‘walks’) denote properties, mostly of individuals. Relations-in-intension, type (RE1…Em)WZ. For example transitive empirical verbs (‘like’, ‘worship’), also attitudinal verbs denote these relations. D-roles, also D-offices, type DWZ, where D (RE). Frequently LWZ. Often denoted by concatenation of a superlative and a noun (‘the highest mountain’). An object A of a type D is denoted ‘A/D’. That a construction C/ n v-constructs an object of type D is denoted ‘C ov D’. We use variables w and t as v-constructing elements of type Z (possible worlds) and W (times), respectively. If C ov DWZ v- constructs an D-intension, the frequently used Composition of the form [[Cw]t], the intensional descent of the D-intension, is abbreviated ‘Cwt’. The analysis of a sentence consists in discovering the logical construction (procedure) encoded by a given sentence. To this end we apply a method of analysis that consists of three steps:7 1) Type-theoretical analysis, i.e., assigning types to the objects that receive mention in the analysed sentence. 2) Synthesis, i.e., combining the constructions of the objects ad (1) in order to construct the proposition of type RWZ denoted by the whole sentence. 3) Type-Theoretical checking. 5 TIL is an open-ended system. The above epistemic base {R, L, W, Z} was chosen, because it is apt for natural-language analysis, but the choice of base depends on the area and language to be analysed. For instance, possible worlds and times are out of place in case of mathematics, and the base might consist of, e.g., R and Q, where Q is the type of natural numbers. 6 We model D-sets and (D1…Dn)-relations by their characteristic functions of type (RD), (RD1…Dn), respectively. Thus an D-property is an empirical function that dependently on states-of-affairs (WZ) picks-up a set of D-individuals, the population of the property. 7 For details see, e.g.,[12]. M. Duží et al. / Ontology As a Logic of Intensions 7
- 22. To illustrate the method, let us analyse the sentence “All drivers are persons”. Ad (1) The objects mentioned by the sentence are individual properties of being a Driver and being a Person, and the quantifier All. Individual properties receive the type (((RL)W)Z), RWZ for short. Given a world-time pair ¢w, t², a property applied to world w and time t returns a class of individuals, its population at ¢w, t². Yet the sentence does not mention any particular individual, be it a driver or a person. It says that the population of drivers is a subset of persons. Thus the type of the (restricted) quantifier All is ((R(RL))(RL)). Given a set M/(RL) of individuals, the quantifier All returns all the supersets of M. Thus we have [0 All 0 M] o (R(RL)). Ad (2) Now we combine constructions of the objects ad (1) in order to construct the proposition (of type RWZ) denoted by the whole sentence. Since we aim at discovering the literal analysis of the sentence, objects denoted by semantically simple expressions ‘driver’, ‘person’ and ‘all’ are constructed by their Trivialisations: 0 Driver, 0 Person, 0 All. By Composing these constructions, we obtain a truth-value (T or F), according as the population of people belongs to the set of supersets of the population of drivers. Thus we have, [[0 All 0 Driverwt] 0 Personwt] ov R. Finally, by abstracting over the values of the variables w and t, we construct the proposition: OwOt [[0 All 0 Driverwt] 0 Personwt]. Ad (3). By drawing a type-theoretical structural tree, we check whether particular constituents of the above Closure are combined in a type-theoretically correct way. Ow Ot [[0 All 0 Driverwt] 0 Personwt] ((R(RL))(RL)) (RL) (R(RL)) (RL) R (RW) ((RW)Z) the type of a proposition, RWZ for short. So much for the method of analysis and the semantic schema of TIL. 1.3. Ontology content Formal ontology is a result of the conceptualization of a given domain. It contains definitions of the most important entities, forms a conceptual hierarchy together with the most important attributes and relations between entities. Material individuals are mereological sums of other individuals, but only contingently so. Similarly, values of attributes and properties are ascribed to individuals contingently, provided a given property is purely contingent, that is without an essential core. Thus we advocate for a (modest) individual anti-essentialism. On the other hand, on the intensional level of propositions, properties, offices and roles, that is entities which we call ‘intensions’, the most important relation to be observed is that of requisite. For instance, the property of being a mammal is a requisite of the property of being a whale. It is an analytically necessary relation between intensions that gives rise to the so-called ISA hierarchy. Thus on the intensional level we advocate for intensional essentialism; an essence of a M. Duží et al. / Ontology As a Logic of Intensions 8
- 23. property is the set of all its requisites. Finally, on the hyper-intensional level of concepts, relations to be observed are equivalence (i.e. producing the same entity), refinement (a compound concept is substituted for a simpler yet equivalent concept), entailment and presupposition. The structure of ontology building starts on the hyper-intensional level with the specification of primitive concepts. Next we specify compound concepts as ontological definitions of entities of a given domain. Having defined entities, we can specify their most important descriptive attributes. The building process continues by specifying particular (empirical) relations between entities and analytical relations of requisites that serve to build up ontological hierarchy. Finally, the most important general rules that govern behaviour of the system are specified. Here again we distinguish analytically necessary constraints from nomic and common necessities that are given by laws and conventions, respectively; they are not valid analytically necessary. For instance, mathematical laws are analytically necessary, they hold independently of states of affairs. On the other hand, laws of physics are not logically or analytically necessary, they are only nomically necessary. It is even disputable whether these laws are eternal in our world. Yet still weaker constraints are, for instance, traffic laws. That we drive on the right-hand side of a lane is valid only by convention and locally. Summarising, basic parts of a formal ontology should encompass: (1) Conceptual (terminological) dictionary which contains: a) primitive concepts b) compound concepts (ontological definitions of entities) c) the most important descriptive attributes, in particular identification of entities (2) Relations a) contingent empirical relations between entities, in particular the part-whole relation b) analytical relations between intensions, i.e., requisites and essence, which give rise to ISA hierarchy (3) Integrity constraints a) Analytically necessary rules b) Nomologically necessary rules c) Common rules of ‘necessity by convention’ Concerning ad (1), in particular ontological definitions, this topic has been dealt with in [4]. Briefly, ontological definition of an entity is a compound construction of the entity. Such a definition often serves as a refinement of a primitive concept of the entity, which makes it possible to prove some analytic statements about the entity. For example, the sentence “Whales are not dolphins” contains the empirical predicates ‘is a whale’ and ‘is a dolphin’, yet the sentence is analytic truth. At no world/time are the properties being a whale and being a dolphin co-instantiated by the same individual. The proposition constructed by the sentence is the necessary proposition TRUE. In order to prove it, we need to refine the concept of a whale. To this end we make use of the fact that the property of being a whale can be defined as the property of being a marine mammal of the order Cetacea that is neither a dolphin nor a porpoise.8 Thus the ontological definition of the property of being a whale is 8 See, for instance, http://mmc.gov/species/speciesglobal.html#cetaceans or http://www.crru.org.uk/education/factfiles/taxonomy.htm M. Duží et al. / Ontology As a Logic of Intensions 9
- 24. OwOt Ox [[0 Mammalwt x] š [0 Marinewt x] š [0 Cetaceawt x] š ™[0 Dolphinwt x] š ™[0 Porpoisewt x]] Types: x o L; Cetacea, Mammal, Marine, Dolphin, Porpoise/(RL)WZ. Using this definition instead of the primitive concept 0 Whale we get: OwOt [0 No Ox [[0 Mammalwt x] š [0 Marinewt x] š [0 Cetaceawt x] š ™[0 Dolphinwt x] š ™[0 Porpoisewt x]] 0 Dolphinwt]. Gloss: “No individual x such that x is a marine mammal of the order Cetacea and x is neither a dolphin nor a porpoise is a dolphin”. In this paper we focus problems ad (2) and (3), that is, we will examine relations between intensions, properties of intensions and various integrity constraints viewed via the logic of intensions. 2. Logic of intensions 2.1. Requisites and ISA hierarchies. It is important to distinguish between purely contingent propositions and the proposition TRUE that takes the value T in all ¢w, t²-pairs. The latter is denoted by analytically true sentences such as the above analysed sentence “No whale is a dolphin” or “All drivers are persons”. We have seen that the literal analysis does not make it possible to prove the analytic truth of the sentence. To this end we have to possibilities. Either we can record ontological definitions refining the primitive concepts of the objects talked about (as illustrated by the above whale-example), or we need to explicitly record in our ontology the fact that there is a necessary relation (-in- extension) between the two properties. We call this relation a requisite, in this case Req1/(R(RL)WZ(RL)WZ) and it receives this definition: [0 Req1 0 Person 0 Driver] =df wt [x [[0 Driverwt x] Š [0 Personwt x]]] Gloss. Being a person is a requisite of being a driver. In other words, necessarily and for any individual x, if x instantiates the property of being a driver then x also instantiates the property of being a person. Now we set out the logic of requisites, because this relation is the basic relation that gives rise to ISA taxonomies.9 The requisite relations Req are a family of relations- in-extension between two intensions, hence of the polymorphous type (RDWZEWZ), where possibly D = E. The relation of a requisite can be defined between intensions of any type. For instance, a requisite of finding is the existence of a sought object. Infinitely many combinations of Req are possible, but the following four are the relevant ones we wish to consider: (1) Req1 /(R (RL)WZ (RL)WZ): an individual property is a requisite of another such property. (2) Req2 /(R LWZ LWZ): an individual office is a requisite of another such office. (3) Req3 /(R (RL)WZ LWZ): an individual property is a requisite of an individual office. (4) Req4 /(R LWZ (RL)WZ): an individual office is a requisite of an individual property. 9 Parts of this section draw on material presented in [5], Chapter 4. M. Duží et al. / Ontology As a Logic of Intensions 10
- 25. Neglecting complications due to partiality, definitions of particular kinds of requisites should be obvious: “Y is a requisite of X” iff “necessarily whatever occupies/ instantiates X at ¢w, t² it also occupies/instantiates Y at this ¢w, t².” Examples. Being a Person and being a Driver is an example of Req1. An example of Req2 is The Commander-in-Chief and the President of USA. The former office is a requisite of the latter, such that whoever is the President is also the Commander-in- Chief. However, it may happen that the Presidency goes vacant, while somebody occupies the office of Commander-in-Chief. As an example of Req3 we can adduce the property of being a US citizen and the office President of USA. Finally, an example of Req4 is the pair of God-office and the property of being Omniscient. Note that while Req1/(R(RL)WZ(RL)WZ) and Req2/(RLWZLWZ) are homogeneous, Req3, Req4 are heterogeneous. Since the latter two do not have a unique domain, it is not sensible to ask what sort of ordering they are. Not so with the former two. We define them as quasi-orders (a.k.a. pre-orders) over (R(RL)WZ), (RLWZ), respectively, that can be strengthened to weak partial orderings. However, they cannot be strengthened to strict orderings on pain of paradox, since they would then both be reflexive and irreflexive. We wish to retain reflexivity, such that any intension having requisites will count itself among its requisites. Since intensions are properly partial functions, in order to deal with partiality we make use of three properties of propositions True, False, Undef/(RRWZ)WZ. If P o RWZ is a construction of a proposition, [0 Truewt P] returns T if the proposition takes the truth- value T in a given ¢w, t², otherwise F. [0 Falsewt P] returns T if the proposition takes the truth-value F in a given ¢w, t², otherwise F. [0 Undefwt P] returns T in a given ¢w, t² if neither [0 Truewt P] nor [0 Falsewt P] returns T, otherwise F. Claim 1 Req1 is a quasi-order on the set of L-properties. Proof. Let X, Y o (RL)WZ. Then Req1 belongs to the class QO/(R(R(RL)WZ(RL)WZ)) of quasi-orders over the set of individual properties: Reflexivity. [0 Req1 X X] = wt [x [[0 Truewt OwOt [Xwt x]] Š [0 Truewt OwOt [Xwt x]]]] Transitivity. [[[0 Req1 Y X] š [0 Req1 Z Y]] Š [0 Req1 Z X]] = [wt [x [[0 Truewt OwOt [Xwt x]] Š [0 Truewt OwOt [Ywt x]]] š [[0 Truewt OwOt [Ywt x]] Š [0 Truewt OwOt [Zwt x]]]] Š wt [x [[0 Truewt OwOt [Xwt x]] Š [0 Truewt OwOt [Zwt x]]]]] In order for a requisite relation to be a weak partial order, it will need to be also anti-symmetric. The Req1 relation is, however, not anti-symmetric. If properties X, Y are mutually in the Req1 relation, i.e., if [[0 Req1 Y X] š [0 Req1 X Y]] then at each ¢w, t² the two properties are truly ascribed to exactly the same individuals. This does not entail, however, that X, Y are identical. It may be the case that there is an individual a such that [Xwt a] v-constructs F whereas [Ywt a] is v-improper. For instance, the following properties X, Y differ only in truth-values for those individuals who never M. Duží et al. / Ontology As a Logic of Intensions 11
- 26. smoked (let StopSmoke/(RL)WZ: the property of having stopped smoking).10 Whereas X yields truth-value gaps on such individuals, Y is false of them: X = OwOt Ox [0 StopSmokewt x] Y = OwOt Ox [0 Truewt OwOt [0 StopSmokewt x]]. In order to abstract from such an insignificant difference, we introduce the equivalence relation Eq/(R(RL)WZ(RL)WZ) on the set of individual properties; p, q o (RL)WZ; =/(RRR): 0 Eq = Opq [x [[0 Truewt OwOt [pwt x]] = [0 Truewt OwOt [qwt x]]]]. Now we define the Req1’ relation on the factor set of the set of L-properties as follows. Let [p]eq = Oq [0 Eq p q] and [Req1’ [p]eq [q]eq] = [Req1 p q]. Then: Claim 2 Req1’ is a weak partial order on the factor set of the set of L-properties with respect to Eq. Proof. It is sufficient to prove that Req1’ is well-defined. Let p’, q’ be L-properties such that [0 Eq p p’] and [0 Eq q q’]. Then [Req1’ [p]eq [q]eq] = [Req1 p q] = wt [x [[0 Truewt OwOt [pwt x]] Š [0 Truewt OwOt [qwt x]]]] = wt [x [[0 Truewt OwOt [p’wt x]] Š [0 Truewt OwOt [q’wt x]]]] = [Req1’ [p’]eq [q’]eq]. Now obviously the relation Req1’ is antisymmetric: [[0 Req1’ [p]eq [q]eq] š [0 Req1’ [q]eq [p]eq]] Š [[p]eq = [q]eq]. Claim 3 Req2 is a weak partial order defined on the set of L-offices. Proof. Let X, Y o LWZ. Then the Req2 relation belongs to the class WO/(R(R LWZLWZ)) of weak partial orders over the set of individual offices. Reflexivity. [0 Req2 X X] = [wt [[0 Occwt X] Š [0 Truewt OwOt [Xwt = Xwt]]]]. Antisymmetry. [[[0 Req2 Y X] š [0 Req2 X Y]] Š [X = Y]] = [wt [[[0 Occwt X] Š [0 Truewt OwOt [Xwt = Ywt]]] š [[0 Occwt Y] Š [0 Truewt OwOt [Xwt = Ywt]]]] Š [X = Y]] Transitivity. [[[0 Req2 Y X] š [0 Req2 Z Y]] Š [0 Req2 Z X]] = [wt [[[0 Occwt X] Š [0 Truewt OwOt [Xwt = Ywt]]] š [[0 Occwt Y] Š [0 Truewt OwOt [Ywt = Zwt]]]] Š wt [[0 Occwt X] Š [0 Truewt OwOt [Xwt = Zwt]]]]. Remark. Antisymmetry requires the consistent identity of the offices constructed by X, Y: [X = Y]. The two offices are identical iff at all worlds/times they are either co- 10 We take the property of having stopped smoking as presupposing that the individual previously smoked. For instance, that Tom stopped smoking can be true or false only if Tom was once a smoker. Similarly for the property of having stopped whacking one’s wife. M. Duží et al. / Ontology As a Logic of Intensions 12
- 27. occupied by the same individual or are both vacant: wt [[0 Truewt OwOt [Xwt = Ywt]] › [0 Undefwt OwOt [Xwt = Ywt]]] = wt ™[0 Falsewt OwOt [Xwt = Ywt]], which is the case here. It is a well-known fact that hierarchies of intensions based on requisite relations establish inheritance of attributes and possibly also of operations. For instance, a driver in addition to his/her special attributes like having a driving license inherits all the attributes of a person. This is another reason for including such a hierarchy into ontology. This concludes our definition of the logic of the requisite relations. We turn now to dealing with a part-whole relation. 2.2. Part-whole relation We advocate for the thesis of modest individual anti-essentialism: If an individual I has a property P necessarily (i.e., in all worlds and times), then P is a constant or partly constant function. In other words, the property has a non-empty essential core Ess, where Ess is a set of individuals that have the property necessarily, and I is an element of Ess. There is, however, a frequently voiced objection to individual anti-essentialism. If, for instance, Tom’s only car is disassembled into its elementary physical parts, then Tom’s car no longer exists; hence, the property of being a car is essential of the individual referred to by ‘Tom’s only car’. Our response to the objection is this. First, what is denoted (as opposed to referred to) by ‘Tom’s only car’ is not an individual, but an individual office/role, which is an intension of type LWZ having occasionally different individuals, and occasionally none, as values in different possible worlds at different times. Whenever Tom does buy a car, it is not logically necessary that Tom buy some one particular car rather than any other. Second, the individual referred to as ‘Tom’s only car’ does not cease to exist even after having been taken apart into its most elementary parts. It has simply lost some properties, among them the property of being a car, the property of being composed of its current parts, etc, while acquiring some other properties. Suppose somebody by chance happened to reassemble the parts so that the individual would regain the property of being a car. Then Tom would have no right to claim that this individual was his car, in case it was allowed that the individual had ceased to exist. Yet Tom should be entitled to claim the reassembled car as his.11 Therefore, when disassembled, Tom’s individual did not cease to exist; it had simply (unfortunately) obtained the property of completely disintegrating into its elementary physical parts. So much for modest individual anti-essentialism. The second thesis we are going to argue for is this. A material entity that is a mereological sum of a number of parts, such as a particular car, is from a logical point of view a simple, hence unstructured individual. Only its design, or construction, is a complex entity, namely a structured procedure. This is to say that a car is not a structured whole that organizes its parts in a particular manner. Tichý says: [A] car is a simple entity. But is this not a reductio ad absurdum? Are cars not complex, as anyone who has tried to fix one will readily testify? No, they are not. If a car were a complex then it would be legitimate to ask: Exactly how complex is it? Now how many parts does a car consist of? One plausible answer which may suggest itself is that it has three parts: an engine, a chassis, and a body. But an equally plausible answer can be given in terms of a much longer list: several spark plugs, several pistons, a 11 As Tichý argues in [16], where he uses the example of a watch being ‘repaired’ by a watchmaker in such a way as to become a key. M. Duží et al. / Ontology As a Logic of Intensions 13
- 28. starter, a carburettor, four tyres, two axles, six windows, etc. Despite being longer the latter list does not overlap with the former: neither the engine, nor the chassis nor the body appears on it. How can that be? How can an engine, for example, both be and not be a part of one and the very same car? There is no mystery, however. It is a commonplace that a car can be decomposed in several alternative ways. … Put in other words, a car can be constructed in a very simple way as a mereological sum of three things, or in a more elaborate way as a mereological sum of a much larger set of things. ([17], pp. 179-80.) It is a contingent fact that this or that individual consists of other individuals and thereby creates a mereological sum. Importantly, being a part of is a relation between individuals, not between intensions. There can be no inheritance or implicative relation between the respective properties ascribed to a whole and its individual parts. Thus it is vital not to confuse the requisite relation, which obtains between intensions, with the part-whole relation, which obtains between individuals. The former relation obtains of necessity (e.g., necessarily, any individual that is an elephant is a mammal), while the latter relation obtains contingently. Logically speaking, any two individuals can enter into the part-whole relation. One possible combination has Saturn a part of Socrates (or vice versa). There will be restrictions on possible combinations, but these restrictions are anchored to nomic necessity (provided a given possible world at which a combination of individuals is attempted has laws of nature at all). One impossible combination would have the largest mountain on Saturn be a part of S (or vice versa). Why impossible? Because of wrong typing: the arguments of the part-whole relation must be individuals (i.e., entities of type L), but the largest mountain on Saturn is an individual office while S is a real number. Yet there is another question interesting from the ontological point of view: which parts are essential for an individual in order to have a property P? For instance, the property of having an engine is essential for the property of being a car, because something designed without an engine does not qualify as a car, but at most as a toy car, which is not a car. The answer to the question which parts are essential in order to have a property P is, in the car/engine example, that the property of having an engine is a requisite of the property of being a car. What is necessary is that a car, any car, should have an engine. It is even necessary that it should have a particular kind of engine, where being a kind of engine is a property of a property of individuals. This kind of a requisite relation should be also included into ontology. What is not necessary is that any car should have some one particular engine belonging to a particular kind of engine: mutatis mutandi, any two members of a particular kind of engine will be mutually replaceable.12 Thus the relation Part_of is of type (RLL)WZ. 2.3. Some other properties of intensions In addition to the above described higher-degree relations of requisite it is also useful to include into ontology some other higher-degree relations between and properties of intensions. In particular, we examine properties of relations-in-intension. For instance, that a given relation is necessarily reflexive, anti-symmetric and transitive, like the partial order induced by a requisite relation. 12 This problem is connected with the analysis of property modification, including being a malfunctioning P. M. Duží et al. / Ontology As a Logic of Intensions 14
- 29. These higher-order properties of intensions are necessarily valid due to the way they are constructed. Since we explicate concepts as closed constructions modulo D- and K- transformation, we can also speak about mutual relations between and properties of concepts which define particular intensions. Those that deserve our attention are in particular: Incompatibility of concepts defining particular properties, i.e., the respective populations are necessarily disjoint; example: bachelor vs. married man. Equivalence of concepts, i.e., the defined properties are one and the same property Week-equivalence of concepts, i.e., the defined properties are ‘almost the same’; as an example we echo the relation Eq between individual properties defined in the previous paragraph Functionality of a relation-in-intension, that is necessarily, in each ¢w, t²-pair, a given relation R Ž Awt uBwt is a mapping fR : Awt Æ Bwt assigning to each element of A at most one element of B Inverse functionality of a relation-in-intension, that is necessarily, in each ¢w, t²- pair, a given relation-in-extension R Ž Awt u Bwt is a mapping fR–1 : Bwt Æ Awt assigning to each element of Bwt at most one element of Awt. We also often need to specify some restrictions on the domain or range of a given mapping. Such local restrictions are specified as integrity constraints which we are going to deal with in the next paragraph.13 2.4. Integrity constraints Classical integrity constraints specify whether a given function-in-intension (i.e. an attribute) must be singular or may be multi-valued, and whether it is mandatory or optional. These constraints are analytically necessary. As an example of a cardinality constraint we can adduce the constraint that everybody has just one (biological) mother and father. That each order must concern a customer, a producer/seller and some products is an example of a constraint on mandatory relation. In addition to these analytical constraints it is useful to specify restrictions on cardinality in case of multi-valued attributes, or particular roles of individuals that enter into a given relation, etc. These constraints have the character of nomically necessary constraints given by some conventions valid in a given domain. For instance, there can be a constraint valid in a given organization that each exporter can have five customers at maximum. Regardless of the character of a given domain, we should always specify the degree of necessity of a given integrity constraint. If C ov R v-constructs the respective condition to be met, the basic kinds of constraints ordered from the highest to the lowest are: a) Analytically necessary rules; these are specified by constructions of the form wt C. b) Nomologically necessary rules; these are specified by constructions of the form Owt C. 13 In the terminology of standard ontology languages, the so-called “properties” are actually relations- in-intension with ‘slots’. Thus we can speak about ‘slot constraints’ and facets that are local slot constraints. See [15]. M. Duží et al. / Ontology As a Logic of Intensions 15
- 30. c) Common rules of ‘necessity by convention’; these are specified by constructions of the form OwOt x [C …x …]. To adduce an example, imagine a mobile agent (typically a car) that encounters an obstacle on his way. In order to specify the behaviour of the agent properly, we must take into account priorities of particular constraints. First, the agent must take into account analytical constraints like that there cannot be two material objects at the same position at the same time. Second, physical laws must be considered; for instance, we must calculate vehicle stopping distance taking into account the speed of the agent as well as of the obstacle and the direction of their move. Only then conventional laws like traffic rules can be considered. If the agent comes to a conclusion that the stopping distance is greater than the distance of an obstacle then, of course, the rules like driving on the right-hand side of a lane or traffic sings cannot be followed. So much for the logic of intensions. In the next section we tackle another important phenomenon that is useful to include into ontology so that reasoning of agents can be properly specified, namely two kinds of entailment relation which also can be viewed as higher-order integrity constraints. They are presupposition vs. mere entailment. 3. Presupposition and entailment When used in a communicative act, a sentence communicates something (the focus F) about something (the topic T). Thus the schematic structure of a sentence is F(T). The topic T of a sentence S is often associated with a presupposition P of S such that P is entailed both by S and non-S. On the other hand, the clause in the focus usually triggers a mere entailment of some P by S. Schematically, (i) S |= P and non-S |= P (P is a presupposition of S); Corollary: If non-P then neither S nor non-S is true. (ii) S |= P and neither (non-S |= P) nor (non-S |= non-P) (mere entailment). More precisely, the entailment relation obtains between hyperpropositions P, S, i.e., the meaning of P is entailed or presupposed by the meaning of S. For the precise definition of entailment and presupposition, see [5], Section 1.5. The phenomenon of topic-focus is associated de dicto – de re ambivalence. Consider a pair of sentences differing only in terms of topic-focus articulation: (1) The critical situation on the highway D1 was caused by the agent a. (2) The agent a caused the critical situation on the highway D1. While (1) not only entails but also presupposes that there be a critical situation on D1, the truth-conditions of (2) are different, as our analysis clarifies. First, (1) as well as (1’), (1’) The critical situation on the highway D1 was not caused by the agent a. are about the critical situation, and that there is a such a situation is not only entailed but also presupposed by both the sentences. As we have seen above, the meaning of a sentence is a procedure producing a proposition, i.e. an object of type RWZ. Execution of this procedure in any world/time yields a truth-value T, F or nothing. Thus we can conceive the sense of a sentence as an M. Duží et al. / Ontology As a Logic of Intensions 16
- 31. instruction on how to evaluate its truth-conditions in any world/time. The instruction encoded by (1) formulated in logician’s English is this: If there is a critical situation on the highway D1 then return T or F according as the situation was caused by the agent a, else fail (to produce a truth-value). Applying our method of analysis introduced in Section 1, we start with assigning types to the objects that receive mention in the sentence. Simplifying a bit let the objects be: Crisis/RWZ: the proposition that there is a critical situation on the highway D1; Cause/(RLRWZ)WZ: the relation-in-intension between an individual and a proposition which has been caused to be true by the individual; Agent_a/L. A schematic analysis of (1) comes down to this procedure: (1s ) OwOt [if 0 Crisiswt then [0 Causewt 0 Agent_a 0 Crisis] else Fail] So far so good; yet there is a problem of how to analyse the connective if-then-else. There has been much dispute over the semantics of ‘if-then-else’ among computer scientists. We cannot simply apply material implication, Š. For instance, it might seem that the instruction expressed by “If 5=5 then output 1, else output the result of 1 divided by 0” received the analysis [[[0 5=0 5] Š [n=0 1]] š [™[0 5=0 5] Š [n=[0 Div 0 1 0 0]]]], where n is the output number. But the output of the above procedure should be the number 1 because the else clause is never executed. However, due to the strict principle of compositionality that TIL observes, the above analysis fails to produce anything, the construction being improper. The reason is this. The Composition [0 Div 0 1 0 0] does not produce anything: it is improper because the division function takes no value at the argument 1, 0. Thus the Composition [n = [0 Div 0 1 0 0]] is v-improper for any valuation v, because the identity relation = does not receive an argument, and so any other Composition containing the improper Composition [0 Div 0 1 0 0] as a constituent also comes out v-improper. The underlying principle is that partiality is being strictly propagated up. This is the reason why the if-then-else connective is often said to be a non-strict function. However, there is no cogent reason to settle for non-strictness. We suggest applying a mechanism known in computer science as lazy evaluation. The procedural semantics of TIL operates smoothly even at the level of constructions. Thus it enables us to specify a strict definition of if-then-else that meets the compositionality constraint. The analysis of “If P then C1, else C2” is a procedure that decomposes into two phases. First, on the basis of the condition P ov R, select one of C1, C2 as the procedure to be executed. Second, execute the selected procedure. The first phase, viz. the selection, is realized by the Composition [0 the_only Oc [[P Š [c=0 C]] š [™P Š [c=0 D]]]]. The Composition [[P Š [c=0 C]] š [™P Š [c=0 D]]] v-constructs T in two cases. If P v-constructs T then the variable c receives as its value the construction C, and if P v- constructs F then the variable c receives the construction D as its value. In either case the set v-constructed by Oc [[P Š [c=0 C]] š [™P Š [c=0 D]]] is a singleton. Applying the singulariser the_only to this set returns as its value the only member of the set, i.e., either the construction C or D. M. Duží et al. / Ontology As a Logic of Intensions 17
- 32. Second, the chosen construction c is executed. As a result, the schematic analysis of “If P then C else D” turns out to be (*) 2 [0 L Oc [[P Š [c=0 C]] š [™P Š [c=0 D]]]]. Types: PoR (the condition of the choice between the execution of C or D); C, D/ n; variable c ov n; the_only/( n(R n)): the singulariser function that associates a singleton set of constructions with the only construction that is an element of this singleton, and which is otherwise (i.e., if the set is empty or many-valued) undefined. Note that we do need a hyperintensional, procedural semantics here. First of all, we need a variable c ranging over constructions. Moreover, the evaluation of the first phase does not involve the execution of the constructions C and D. These constructions are only arguments of other constructions. Returning to the analysis of (1), in our case the condition P is that there be a crisis on the highway D1, i.e., 0 Crisiswt. The construction C that is to be executed if P yields T is [0 Causewt 0 Agent_a 0 Crisis]], and if P yields F then no construction is to be selected. Thus the analysis of the sentence (1) comes down to this Closure: (1*) OwOt 2 [0 LOc [[0 Crisiswt Š [c = 0 [0 Causewt 0 Agent_a 0 Crisis]]]] š [™0 Crisiswt Š 0 F]]] The evaluation of (1*) in any ¢w, t²-pair depends on whether the presupposition 0 Crisiswt is true in ¢w, t². If true, then the singleton v-constructed by Oc [ … ] contains as the only construction the Composition [0 Causewt 0 Agent_a 0 Crisis]], which is afterwards executed to return T or F, according as the agent a caused the crisis. If false, then the second conjunct in Oc […] comes down to [0 T Š 0 F] and thus we get Oc 0 F. The v-constructed set is empty. Hence, 2 [LOc 0 F] is v-improper, that is the Double Execution fails to produce a truth-value. To generalise, an analytic schema of a sentence S associated with a presupposition P is a procedure of the form If P then S else Fail. The corresponding schematic TIL construction is (**) OwOt 2 [0 LOc [[Pwt Š [c=0 Swt]] š [™Pwt Š 0 F]]]. The truth-conditions of the other reading, i.e. the reading of (2) (2) “The agent a caused the critical situation on the highway D1” are different. Now the sentence (2) is about the agent a (topic), ascribing to a the property that it caused the crisis (focus). Thus the scenario of truly asserting that (2) is not true can be, for instance, this. Though it is true that the agent a is known as a hit and run driver, this time he behaved well and prevented a critical situation from arising. Or, a less optimistic scenario is thinkable. The critical situation on D1 is not because of the agent a’s risky driving but because the highway is in a very bad condition. Hence, that there is a crisis is not presupposed by (2), and its analysis is this Closure: (2*) OwOt [0 Causewt 0 Agent_a 0 Crisis] M. Duží et al. / Ontology As a Logic of Intensions 18
- 33. The moral we can extract from these examples is this. Logical analysis cannot disambiguate any sentence, because it presupposes full linguistic competence. Thus we should include into our formal ontology the schematic rules that accompany activities like agents’ seeking and finding, causing something, etc. Then our fine-grained method can contribute to a language disambiguation by making these hidden features explicit and logically tractable. In case there are more non-equivalent senses of a sentence we furnish the sentence with different TIL constructions. If an agent receives an ambiguous message, he/she can answer by asking for disambiguation. Having a formal fine-grained encoding of a sense, the agent can then infer the relevant consequences. 4. Conclusion The theoretical specification of particular rules is only the first step. When making these features explicit we keep in mind an automatic deduction that will make use of these rules. To this end we currently develop a computational FIPA compliant variant of TIL, the functional programming language TIL-Script (see [3]). The direction of further research is clear. We are going to continue the development the TIL-Script language in its full-fledged version equivalent to TIL calculus. The development of TIL-Script is still a work in progress, in particular the implementation of its inference machine. From the theoretical point of view, the calculus and the rules of inference have been specified in [5], Sections 2.6 and 2.7. Yet its full implementation is a subject of further research. Currently we proceed in stages. First we implemented a method that decides a subset of the TIL-Script language computable by Prolog (see [2]). This subset has been now extended to the subset equivalent to standard FOL. For ontology building we combine traditional tools and languages like OWL (Ontology Web Language) with TIL-Script. We developed an extension of the editor Protégé-OWL so that to create an interface between OWL and TIL-Script. The whole method has been tested within the project ‘Logic and Artificial Intelligence for Multi-Agent Systems’ (see http://labis.vsb.cz/) using a traffic system as a case study. The sample test contained five mobile agents (cars), three car parks and a GIS agent. The GIS agents provided mobile agents with ‘visibility’, i.e., the coordinates of the objects within their visibility. All the agents communicated in TIL- Script and started with minimal (but not overlapping) ontologies. During the test they learned new concepts and enriched their ontology in order to be able to meet their goals. The agents’ goal was to find a vacant parking lot and park the car. All the agents succeeded and parked in a few seconds, which proved that the method is applicable and usable not only as an interesting theory but also in practice. Acknowledgements. This research has been supported by the Grant Agency of the Czech Republic, projects No. 401/09/H007 ‘Logical Foundations of Semantics’ and 401/10/0792, ‘Temporal aspects of knowledge and information’, and by the internal grant agency of FEECS VSB-Technical University Ostrava, project No. IGA 22/2009, ‘Modeling, simulation and verification of software processes’. M. Duží et al. / Ontology As a Logic of Intensions 19
- 34. References [1] Baader, F., Calvanese, D., McGuinness, D., L., Nardi, D., and Patel-Schneider, P., F., editors. The Description Logic Handbook: Theory, Implementation and Application. Cambridge University Press, 2002. [2] íhalová, M., Ciprich, N., Duží, M., Menšík, M. (2009): Agents' reasoning using TIL-Script and Prolog. In 19th Information Modelling and Knowledge Bases, ed. T. Tokuda, Y. Kiyoki, H. Jaakkola, T. Welzer, Družovec, Slovenia: University of Maribor, 137-156. [3] Ciprich, N., Duží, M. and Košinár, M.: The TIL-Script language. In Kiyoki, Y., Tokuda, T. (eds.): EJC 2008, Tsukuba, Japan 2008, pp. 167-182. [4] Duží, M., Materna, P. (2009): Concepts and Ontologies. In Information Modelling and Knowledge Bases XX . Y. Kiyoki, T. Tokuda, H. Jaakola, X. Chen, N. Yoshida (eds.), Amsterdam: IOS Press, pp. 45-64. [5] Duží, M., Jespersen, B. and P. Materna: Procedural Semantics for Hyperintensional Logic; Foundations and Applications of Transparent Intensional Logic. Springer: series for Logic, Epistemology and the Unity of Science, Vol. 17, 2010, ISBN: 978-90-481-8811-6. [6] Gordon, M. J. C. and Melham, T. F. (eds.) 1993: Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge: Cambridge University Press. [7] Hayes, P., Menzel, C., 2001. Semantics of knowledge interchange format. In: IJCAI 2001 Workshop on the IEEE Standard Upper Ontology. [8] Horrocks, I. and Patel-Schneider, P.F. 2003: Three These of Representation in the Semantic Web. WWW2003, May 20-24, Budapest, Hungary, 2003, (retrieved 10.1.2005) URL: http://www2003.org/cdrom/papers/refereed/p050/p50-horrocks.html. [9] Horrocks, I., Patel-Schneider, P.F., Boley, H., Tabet, S., Grosof, B. and Dean, M 2004: SWRL: A Semantic Web Rule Language Combiming OWL and RuleML. W3C Member Submission, May 2004, (retrieved 10.1.2010), URL: http://www.w3.org/Submission/SWRL/. [10] Jespersen, B. (2008): ‘Predication and extensionalization’. Journal of Philosophical Logic, vol. 37, 479 – 499. [11] Kifer, M., Lausen, G., and James Wu. Logical foundations of object-oriented and frame-based languages. Journal of the ACM, 42(4):741-843, 1995. [12] Materna, P. and Duží M. (2005): ‘The Parmenides principle’, Philosophia, 32, 155-80. [13] Paulson. L. C. 1994: Isabelle: A Generic Theorem Prover. Number 828 in LNCS. Berlin: Springer. [14] Sowa, John, F.: Knowledge Representation. Logical, Philosophical, and Computational Foundations. Brooks/Cole 2000. [15] Svátek, V. Ontologie a WWW. www source: http://nb.vse.cz/~svatek/onto-www.pdf [16] Tichý, P. 1987. Individuals and their roles (in German; in Slovak in 1994). Reprinted in (Tichý 2004: 710-748). [17] Tichý, P. 1995. Constructions as the subject-matter of mathematics. In The Foundational Debate: Complexity and Constructivity in Mathematics and Physics, eds. W. DePauli-Schimanovich, E. Köhler and F. Stadler, 175-185. Dordrecht, Boston, London, and Vienna: Kluwer. Reprinted in (Tichý 2004: 873-885). [18] Tichý, P. 2004. Collected Papers in Logic and Philosophy, eds. V. Svoboda, B. Jespersen, C. Cheyne. Prague: Filosofia, Czech Academy of Sciences, and Dunedin: University of Otago Press. [19] W3C 2004: The World Wide Web Consortium: OWL Web Ontology Language Overview W3C Recommendation 10 February 2004, (retrieved 10.1.2010) URL: http://www.w3.org/TR/owl- features/. M. Duží et al. / Ontology As a Logic of Intensions 20
- 35. A Three-layered Architecture for Event-centric Interconnections among Heterogeneous Data Repositories and its Application to Space Weather Takafumi NAKANISHIa , Hidenori HOMMAa , Kyoung-Sook KIMa , Koji ZETTSUa , Yutaka KIDAWARAa and Yasushi KIYOKIa,b a National Institute of Information and Communication Technology(NICT), Japan b Keio University, Japan Abstract. Various knowledge resources are spread to a world-wide scope. Unfortunately, most of them are community-based and never thought to be used among different communities. That makes it difficult to gain “connection merits” in a web-scale information space. This paper presents a three-layered system architecture for computing dynamic associations of events to related knowledge resources. The important feature of our system is to realize dynamic interconnection among heterogeneous knowledge resources by event-driven and event-centric computing with resolvers for uncertainties existing among those resources. This system navigates various associated data including heterogeneous data-types and fields depending on user's purpose and standpoint. It also leads to effective use for the sensor data because the sensor data can be interconnected with those knowledge resources. This paper also represents application to the space weather sensor data. Keywords. Event-centric interconnections, heterogeneous data repositories, three- layered architecture, uncertainties for interrelationships, space weather sensor data Introduction A wide variety of knowledge resources are spread to a worldwide scope via Internet with WWW. Most knowledge resources are provided through community-based creation and they are not shared and used well among different communities. In fact, most data repositories are constructed and used in the local community independently. It is difficult for users to interconnect these widely distributed data according to their purposes, tasks, or interests. That makes it difficult to gain “connection merits” in a web-scale information space. The difficulty in retrieving and interconnecting various knowledge resources arises because of heterogeneities of data-types, contents and utilization objectives. Recently, various sensor data resources are also created widely and spread to the worldwide areas. It is becoming very important to find how to utilize them in related applications. For specialists in different fields from the community sharing the sensor data, it is difficult to use those data effectively because their usage and definitions are not clearly recognized. Each research community focuses on the sensor for research Information Modelling and Knowledge Bases XXII A. Heimbürger et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-690-4-21 21
- 36. purpose dependent of the community. In the current state, most sensor data are not used effectively widely because each research community installs the sensor of each research purpose. It is necessary to share the sensor data with the information on the purpose of use and the background knowledge. For users in the other fields, it is difficult to understand how the sensor data are related to their lives and what the sensor data means. Generally, the expression of the sensor data is an enumeration of the numerical values with domain-specific formatting. For making it possible to utilize those data by other domain-specialists, it is important to show what the sensor data mean and what influence the sensor data cause. Some methods of annotating and connecting the sensor data are expected directly. However, it is too hard and complex. An interpretation and utilization of the sensor data are different according to user's background knowledge and his/her purposes. It is important to realize interconnection mechanisms depending on user's background knowledge and his/her purpose for sensor data. Currently, we have organized a joint research with the Space Environment Group of NICT, to solve how to share sensor data related to the space weather field. The aim of this research is to create new applications of space-weather sensor-data by combining the related knowledge resources. Space Environment Group of NICT is delivering sensor data of solar activities and space environment that is called space weather by RSS [1]. Space weather shows conditions on the Sun and in the solar wind, magnetosphere, ionosphere, and thermosphere. These can endanger human life or health by affecting the performance and reliability of space-borne and ground-based man-made systems [2] such as communication failure, damage of electric devices for space satellite, bombing, etc. The group is delivering these data so that various users may use them. In our current global environment, it is important to transmit significant knowledge to actual users from various data resources. In fact, most events affect various aspects of other areas, fields and communities. For example, in the case of the space weather, a sensor data representing abnormality of Dst index, which is one of the sensor data on the space weather related to Geomagnetic storm event, and news articles on interruption of relay broadcast for XVI Olympic Winter Games are interrelated in the context of “watching TV.” The Dst index and those news articles are individually published from different communities. In order to understand a concept in its entirety on user’s standpoint, a user would need to know the various interrelationships between data in interdisciplinary fields. By only using existing search engines, however, it is difficult to find various data resources in interdisciplinary fields. Moreover, the interconnection will change over time. In order to manage ever-changing interrelations among a wide variety of data repositories, it is important to realize an approach for discovering “event-centric interrelations” of various types of data on each different community depending on user’s standpoint. In this paper, we present a three-layered system architecture for computing dynamic associations of events in nature to related knowledge resources. The important feature of our system is to realize dynamic interconnection among heterogeneous data resources by event-driven and event-centric commuting with resolvers for uncertainties existing among those resources. This realizes interconnection indirectly and dynamically by semantic units for the data of various types such as text data, multimedia data, sensor data etc. In other words, it navigates various appropriate data including data of heterogeneous data-type and heterogeneous fields depending on user's purpose and standpoint. In addition, it leads to effective use for the sensor data because T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 22
- 37. the sensor data are interconnected with various data. We also propose a three-layer data structure for representing semantic units extracted from all type of data. The data structure represents semantic units depending on a constraint in each layer. By this data structure, we can compute interconnection between heterogeneous data in some semantic units. Actually, we consider that it is difficult to construct only static basic interrelationships that are acceptable in any cases. It is effective to provide the interrelationships corresponding to user’s standpoint dynamically. The essence of our system is to dynamically select, integrate and operate various appropriate content resources for distributed environment. We define constraints in each layer of the three- layer data stricture for semantic units –event, occurrence and scene. Therefore, our framework is important and effective to realize the distributed heterogeneous data resources. This paper is organized as follows. In section 1, we present a three-layer data structure for interconnection. ries. In section 2, we present the overview of interconnection for heterogeneous content repositories. In section 3, 4, and 5, we describe detail data structures and operations of an event, an occurrence, and a scene. In section 6, we describe the related works. Finally, in section 7, we conclude this paper. 1. Three-layer Data Structure for Interconnection In this section, we present a three-layer data structure for realizing event-centric interconnection of heterogeneous data repositories. Currently, a relationship between each data is represented in a static link. We consider that there are limitations to uniquely represent global static interrelationships. Because interrelationships keep changing in various factors such as spatiotemporal condition, background field, situation. Of course, the interrelation that everyone supports might exist, too. However, it is important to dynamically represent interrelationships depending on an arbitrary situation. It is difficult to represent unique and global interrelationship because it has uncertainties. We define the constraint for reducing the uncertainties, and design the method for representation of various interrelationships. In section 1.1, we describe uncertainties for interrelationships between heterogeneous data. In section 1.2, we define a three-layer data structure for interrelationships that considers these uncertainties. Furthermore, in section 1.3, we consider why we apply interconnection not integration from the standpoint of three uncertainties. 1.1. Uncertainties of Interrelationships between Heterogeneous Data Generally, it is difficult to represent static interrelationships between heterogeneous data because it has uncertainties. However, most current systems utilize static link representation. They implicitly have limitation of interconnection such as limitation of domain, data-type, and field. For realizing interconnection between heterogeneous data, we have to clear uncertainty items. There are three uncertainties for interrelationship between heterogeneous data as follows: (1) Which part of data to focus on. T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 23
- 38. It is necessary to extract metadata set as a semantic unit from target data in order to target heterogeneous data. In this case, the extracted semantic unit depends on which part of data to focus on. For example, it is assumed to extract semantic unit from the sensor data of precipitation. In the case that you focus when precipitation is zero, you can detect semantic unit that represents fine or cloudy weather. In the case that you focus when precipitation is higher than the threshold, you can detect semantic unit that represents heavy rain. A different semantic unit can be extracted from the same data source by changing the constraint. That is, it is important to clarify focus point of the data as constraint. (2) What standpoint to interpret data. An interpretation of each extracted semantic unit is changing by user’s background knowledge, standpoint, etc. For example, it assumes that there are disaster ontology and climate changing ontology. When the heavy rain semantic unit is mapped to disaster ontology, the event will be semantically arranged close to swollen river, traffic damage, etc. When the same heavy rain semantic unit is mapped to climate changing ontology, the event will be semantically arranged close to global warming. By this example, you can find various interpretations of the semantic unit are possible by changing the constraint. That is, it is important to clarify what standpoint to interpret data as constraint. (3) What standpoint to interrelate between each data. An interrelationship of each extracted semantic unit is also changing by user’s background knowledge, standpoint, etc. Actually, most interconnection depends on a situation. In such case, we should represent the interrelationship according to the situation. That is, it is important to clarify what standpoint to interrelate between each data as constraint. We consider that we can uniquely represent an interconnection on the constraints if we apply the constraints that exclude three above-mentioned uncertainties. Therefore, it is important to design a data structure for defining the constraints that represent three uncertainties. 1.2. Three-layer Data Structure—Event, Occurrence and Scene For representing interrelationship between heterogeneous data with such three uncertainties, we realize event-centric interconnection for heterogeneous data. It is necessary to design a new data structure for solving the uncertainties. In this section, we design a new three-layer data structure for interconnection of heterogeneous data. The data structure consists of three layer based on three uncertainties. By this data structure, we can represent interconnection between heterogeneous data depending on user’s purpose and standpoint. The data structure consists of three data-types in each layer –event, occurrence and scene. Figure 1 shows overview of the data structure and its layers. Each data has constraints – condition, context and viewpoint. à Event An event is a minimum semantic unit extracted from delivered target data. An event consists of set of various metadata that represent its features. For detecting event from target data, we have to determine a constraint. The constraint for event detection is called a condition. The condition represents which part of target data to focus on. In other words, the condition is constraints that represent T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 24
- 39. how to summarize target data and how to composite an event. Various events can be detected by setting various conditions from same target data. That is, this solves uncertainty (1) shown in section 1.1. The event also has its condition. It becomes possible to process unitedly by making various different kinds of data resources an event. à Occurrence An occurrence is a projected event according to a constraint that is called context. The interpretation of the event is different according to the standpoint, the background knowledge, etc. The context is a constraint for uniquely providing the interpretation of an event such as user's standpoint, background knowledge, etc. A occurrence is projection data of event along context. That is, the context solves uncertainty (2) shown in section 1.1. By the context, we can specify semantic of an event. Conversely, various occurrences can be composited by setting various contexts from same event. The occurrence consists of projected metadata with contexts. à Scene A scene is set of relationships between occurrences according to a constraint that is called viewpoint. The interconnection of occurrences is different according to the standpoint, the background knowledge, etc. The viewpoint is a constraint for uniquely providing the interconnection of occurrences such as user's standpoint, background knowledge, etc. That is, the viewpoint solves uncertainty (3) shown in section 1.1. By the viewpoint, we can specify interconnection. Conversely, various scenes can be composited by setting various viewpoints from same occurrences. The various interconnections between heterogeneous data can be represented by this data structure of three layers. For representing interconnection between heterogeneous data, events are detected from target data according to condition; occurrences are constructed by projection of events according to context; and scenes Figure 1. Overview of three-layer data structure for interconnection. The data structure consists of event, occurrence, and scene. There are three types of constraint – condition, context and viewpoint –for avoiding the uncertainties. T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 25
- 40. are constructed by interconnection of each occurrence according to viewpoint. The interconnection of heterogeneous data in the three constraints – condition, context and viewpoint– can be found if tracing this data structure oppositely according to the three constraints. 1.3. Integration or Interconnection Generally, techniques for arranging two or more resources include integration and interconnection. In this section, we consider whether integration or interconnection is effective in this case. Table 1 shows a summary for general features of integration and interconnection. For realizing an integration technique, we have to reconstruct all system in most cases because it is necessary to consolidate the system that distributes. However, an integration technique provides efficient computation for arranging two or more resources. An integration technique can arrange static, usual interrelationships fast. Oppositely, it is not possible to apply to the arrangement of various dynamic relationships. On the other hand, it is easy to implement an interconnection technique in most case because it is possible to mount making the best use of existing systems. However, the computational complexity tends to increase. It is better to apply an integration technique not an interconnection technique to arrange static, usual interrelationships because there are a lot of computational complexities. It is possible to apply an interconnection technique to arrangement of various dynamic interrelationships. In this paper, we focus on interrelationships of heterogeneous data. It is difficult to represent static interrelationships between heterogeneous data because it has the uncertainties shown in section 1.1. In this assumption, we should present the method for representing various interrelationships that change dynamically depending on the various constraints by avoiding these uncertainties. The interconnection can realize such an environment. Recently, a lot of data repositories and resources have been widely spread on the Internet. It is difficult to integrate these environments. Of course, it is not impossible to construct the integration system with a part of them. From the standpoint of the extendibility, it is reasonable to apply the interconnection to this environment that increases every day. An interconnection can be applied without changing the arrangement of the resource of the distributed environment. Actually, effectively using the heterogeneous data repositories scattered in the distributed environment is becoming important. In this case, we also take care of three uncertainties for interrelationship. In the case of space weather sensor data derived by Space Table 1. Summary of integration and interconnection T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 26
- 41. Environment Group of NICT, we are grappling with the similar issue. They require also representing various relationships between their space weather sensor data and other data. Furthermore, we are working “knowledge cluster systems” for knowledge sharing, analysis, and delivery among remote knowledge sites on a knowledge grid [3]. In this environment, we have constructed and allocated over 400 knowledge bases to each site. One of the important issues in this environment is how to arrange and interrelate among these knowledge bases. We have proposed a viewpoint-dependent interconnection method of knowledge bases by focus on concept words in each knowledge base [4]. In this case, to arrange each knowledge base maintaining a distributed environment, the interconnection is applied. Therefore, in order to compute interrelation among various resources in distributed environment, it is important to realize an interconnection mechanism depending on some constraint for avoiding uncertainties. 2. Overview of Interconnection for Heterogeneous Content Repositories In this section, we describe an overview of event-centric interconnection of heterogeneous content repositories. This is a model for interconnection of interdisciplinary data resources in distributed environment depending on some constraint for avoiding uncertainties shown in section 1. In today’s global environment, it is important to transmit significant knowledge to actual users from various data resources. In order to realize this environment, it is important to interrelate among data resources depending on some constraint for avoiding uncertainties. This framework realizes interconnection indirectly and dynamically for the data of various types such as text data, multimedia data, sensor data etc. That is, it helps a user to obtain various appropriate data including data of heterogeneous data-type and heterogeneous fields depending on user's purpose and standpoint. The overview of an event-centric interconnection for heterogeneous contents repositories is shown in Figure 2. Here, for realizing the framework, there are four modules – event detection module, event projection module, correlation analysis module and codifier module. à Event detection module: An event detection module extracts events shown in section 1.2 from target data depending on a condition. The condition is a kind of constraint for avoiding uncertainty shown in section 1. The event detection module can composite various events by setting various condition from same target data. The diversity of data itself that is one of the uncertainties when an event is extracted is avoided by a condition. The input of the module is target data. It must be set in each data repository. The output of the module consists of extracted event set. It is possible to process unitedly by making various heterogeneous data resources an event. à Event projection module: An event projection module projects detected event depending on a context. We call a projected event a occurrence shown in section 1.2. The projection process corresponds to the interpretation of the event according to the context. For example, it assumes that an event detection module extracts a heavy rain event from article data and there are disaster ontology and climate changing ontology. When a context is disaster, heavy rain event will be projected in disaster ontology, and construct a new occurrence. The occurrence T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 27
- 42. will be semantically arranged close to swollen river, traffic damage, etc. When a context is climate changing, heavy rain event will be projected in climate changing ontology, and construct a new occurrence. The occurrence will be semantically arranged close to global warming. In these two case, an event projection module projects thematic metadata described in the heavy rain event to each ontology as a new occurrence. When a context is a spatiotemporal constraint, a new occurrence may be constructed as a shape that represents spatiotemporal region on 3D axis (latitude, longitude, and time) from heavy rain event. In this case, an event projection module projects spatiotemporal metadata described in the heavy rain event to 3D shape as a new occurrence. An event projection module can composite various occurrences by setting various contexts from same event. The occurrence consists of projected metadata with contexts. à Correlation analysis module: A correlation analysis module interconnects occurrences depending on a viewpoint based on computing correlation. We call a set of interconnection between occurrences a scene shown in section 1.2. The interconnection of occurrences is different according to the standpoint, the background knowledge, etc. The viewpoint is a constraint for uniquely providing the interconnection of occurrences such as user's standpoint, background knowledge, etc. By the viewpoint, we can specify interconnection. Conversely, A correlation analysis module can composite various scenes by setting various viewpoints from same occurrences. This module can indirectly interconnect heterogeneous data by utilizing occurrences. à Codifier module: A codifier module arranges and organizes scenes extracted from a correlation analysis module. The interconnection of heterogeneous data in Figure 2. The overview of an event-centric interconnection for heterogeneous contents repositories. This method consists of four modules—event detection module, event projection module, correlation analysis module, and codifier module. T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 28
- 43. the three constraints – condition, context and viewpoint– can be found if tracing this data structure oppositely according to the three constraints. The process of event-centric interconnection of heterogeneous content repositories is described as follows: Step1. Detecting events from heterogeneous data An event detection module extracts an event from target data along an event class database. In the event class database, event models and their conditions are stored. This step produces semantic units that are unified data-type from various data as events. By this step, it is possible to process unitedly by making various heterogeneous data resources an event. Step2. Projecting events as occurrences An event projection module projects detected event along a occurrence class database. In the occurrence class database, occurrence models and their context are stored. This step produces projected events as occurrences. An event projection module can composite various occurrences by setting various contexts. An occurrence is an event interpreted by the context by projection. Therefore, for representing various interconnections, this step should produce various occurrences from a same event. Step3. Interconnecting occurrences as scenes A correlation analysis module interconnects occurrences depending on a viewpoint along a scene class database. In the scene class database is stored scene models and their viewpoints. This step produces interconnection set of occurrences as scenes. This step can composite various scenes by setting various viewpoints from same occurrences. This set can indirectly interconnect heterogeneous data represented in interconnection set of occurrences. Step4. Providing organized scenes as event-centric interrelationships between heterogeneous data A codifier module arranges and organizes scenes extracted from a correlation analysis module. When a user gives some queries representing a condition, a context and a viewpoint, this step provides appropriate scene set dynamically. By this process, a user obtains interconnection between heterogeneous data depending on three constraints for avoiding uncertainties. Figure 3 shows three important operations for representation of interrelationships between heterogeneous data. These are detection, projection and interconnection. Each operation has a constraint—condition, context, and viewpoint. On the viewpoint from target data, it is possible to expand various interconnections of target data by these constraints. Conversely, on the viewpoint from a user, it is possible to narrow interconnections candidate of target data by these constraints. The computation result by this process can represent relationships between heterogeneous data by utilizing scene data in RDF etc. With regard to each step, any method is acceptable. Please note that this process dynamically represents interrelationships between heterogeneous data depending on a condition, a context and a viewpoint. Conversely, by this process, we can find the approval constraints for the interrelationships (e.g. which data, which part of data, what standpoint to interpret data, and what standpoint to interrelate). This process dynamically represents various interconnections with the condition, context, and viewpoint. That is, it helps a user to obtain various appropriate data including data of heterogeneous data-type and T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 29
- 44. heterogeneous fields depending on user's purpose and standpoint while user’s understanding. 3. Event—Detection Figure 4 shows an overview of event detection. An event is extracted from target data by an event model and its condition in event class database shown in Figure 2. An event consists of seven attributes as follows: event=eventLabel, eventType, date, place, keywords, source, condition, where eventLabel means the name of the event, eventType means the kind of the event and represents to which an event model to belong, date means temporal annotations, place means spatial annotations, keywords represents thematic annotations, source means URI of source data, and condition represents condition expression used for the event detection. Please note that not only each detected event but also each event model stored in event class database shown in Figure 2 has same seven attributes. These event models are used as basic patterns when the events are extracted. These attributes are roughly divided into the basic attribute (eventLabel) that represents basic information, the feature attributes (date, place, keywords) that represent the feature of the event and the origin attributes (eventType, source, condition) that represent how to extract themselves. That is, an event consists of two Figure 4. Overview of an event and its condition. An event data extracted from target data depending on event model including condition. An event consists of a basic attribute (e.g. event label), feature attributes (e.g. date, place, keywords), and origin attributes (e.g. event type, source and condition). Figure 3. Three important operations for representation of interrelationships between heterogeneous data— detection, projection and interconnection— and the data structure. T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 30
- 45. types of attribute—feature attribute and origin attribute. The feature attributes are used for interconnecting target data that is represented by event. The origin attributes are used to navigate source data and represent as reason. Furthermore, each attribute is permitted to have two or more elements. The elements given to each attributes are roughly classified into two types—inheritance element and data dependence element. The inheritance element is an element decided depending on the event model. Both events extracted by using the same event model have the same elements. These elements are called inheritance elements because they are inherited from the model. That is, the inheritance element represents features of its event type. The data dependence element is extracted from target data itself. Elements of this type change depending on the target data even if both events are extracted from the same event model. That is, data dependence element represents features of itself. An event is detected from target data by using a condition in each event module; some elements of each attribute are inherited from event module; and some other elements of each attribute are extracted from the target data. By this process, it is possible to unitedly process various heterogeneous data resources by extracting minimum semantic units as event. 4. Occurrence—Projection Figure 5 shows an overview of projection of an event as occurrences. An occurrence is a projected event by occurrence models including its context in occurrence class database shown in Figure 2. The occurrence model represents how to project events in each context. An occurrence represents as follow: occurrence=occurrenceLabel, occurrenceType, attr1’, attri2’,…, attrin’, eventSource, context, where occurrenceLabel means the name of the occurrence, occurrenceType means the kind of the occurrence and represents to which occurrence models to belong, eventSource means URI of target event data, context represents context expression used for the event projection as the occurrence, and an attrii’ represents projected feature attributes depending on a context.As with an event, a occurrence has three types of Figure 5 Overview of occurrences and their contexts. An occurrence is projected event depending on a context. T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 31
- 46. attributes— a basic attribute (occurrenceLabel), feature attributes (attrii’), and origin attributes (occurrenceType, eventSource, context). Please note that feature attributes set of a occurrence foccurrence is changing depending on an occurrence model including a context Pcontext. foccurrence=(attri1’, attri2’,…, attrin’)= Pcontext (fevent), fevent=(attri1, attri2,…, attrim), where attrij is feature attribute of an event, attrii’ is feature attribute set of a occurrence, and Pcontext. is an occurrence model with a context. That is, an occurrence model Pcontext. projects event feature attributes attrij to occurrence feature attributes attrii’. Various occurrences can be composited by setting various occurrence models with contexts from same event. Composing various occurrences by using various occurrence models depending on the context means various interpretations of an event are introduced. Therefore, for representing various interconnections, various occurrences should be produced from a same event. When this data structure applies to the system, you can uniquely clarify interpretation of an event by a context that represents user's standpoint, background knowledge, etc. We specify semantic of an event by a occurrence. 5. Scene —Interconnection Figure 6 shows an overview of a scene. A scene is a record including interrelationship of occurrences by a scene model including its viewpoint in scene class database shown in Figure 2. A scene represents as follow: Scene=sceneLabel, scenType, interrelationship, viewpoint, Interrelationship=fromOccurrenceURI, toOccurrenceURI, where sceneLabel means the name of the scene, sceneType means the kind of the scene and represents to which scene models to belong, interrelationship means an interrelationship of maters, and viewpoint represents viewpoint expression used for the occurrence interconnection as the scene. The interrelationship has two types of occurrences. It consists of fromOccurrenceURI that represents cause occurrences for relationship and toOccurrenceURI that represents effect occurrences for relationship. Figure 6. Overview of a scene and its viewpoint. A scene is a record including an interrelationship between occurrences T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 32
- 47. Please note that not only each scene but also each scene model stored in scene class database shown in Figure 2 has same attribute sets. These scene models are used as basic patterns when the occurrences are interconnected by correlation analysis. Various scenes can be composited by setting various viewpoints from same occurrences. This data set can indirectly interconnect heterogeneous data represented in interconnection set of occurrences. When this data structure applies to the system, you can uniquely clarify interrelationships of a occurrence by a viewpoint that represents user's standpoint, background knowledge, etc. We specify interconnection of occurrences by a scene. This process dynamically represents interrelationships between heterogeneous data depending on a viewpoint. Conversely, we can find the approval viewpoints for the interrelationships. 6. Implementation Example—Application to the Space Weather Figure 7 shows an implementation for interconnection of heterogeneous contents repositories applying to space weather data as an example. Currently, we are co- working with the Space Environment Group of NICT. Space Environment Group of NICT is delivering sensor data of solar activities and space environment that is called space weather by RSS. One of the important problems is groping for effective use of the space weather data. One of the effective uses is to show how the event that these sensors represent influences our life of every day. For realizing it, we are developing an interconnection method for space weather sensor data and other data such as meteorological sensor data, general newspaper article, etc by using the three-layered architecture. It means this system bridges the gap between general facts such as events in our life of everyday and concepts in specific field such as space weather sensor data. In Figure 7, the system consists of event extraction modules, a correlation analysis management module, correlation analysis modules and codifier module. à Event extraction modules Each event extraction module detects events from each data such as news article data, meteorological sensor data that are AMeDAS (Automated Meteorological Data Acquisition System) data by Japan Meteorological Agency, Space weather sensor data, etc. These modules produce semantic units shown in section 3 that are unified data-type from various data as events. à Correlation analysis management module A correlation analysis management module has two operations. One is projection of each detected event data to correlation analysis modules as occurrences. An occurrence is an event interpreted by the context by projection. Another is organization of correlation analysis modules. In this system, various types of correlation analysis modules provide various scenes that represent interrelationships between occurrences (projected events). The correlation analysis management module should organize these data. That is, this module is input/output interfaces for correlation analysis modules. à Correlation analysis modules A correlation analysis module interconnects occurrences depending on a viewpoint. In this system, we are developing two types of correlation analysis modules—spatiotemporal correlation analysis module and semantic correlation analysis module. Spatiotemporal correlation analysis module T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 33
- 48. A spatiotemporal correlation analysis module is an analysis module that specializes in the axis of time and spaces. This finds interrelationships of the projected events (occurrences) into which the region and time hour by hour change as phenomenon. We are developing this module based on a moving phenomenon model [5] Semantic correlation analysis module A semantic correlation analysis module is an analysis module that specializes in the semantics. This finds interrelationships of the projected events (occurrences) depending on viewpoint. We are developing this module based on this reference [4] The interrelation is extracted by mutual constraint between these analysis modules. à Codifier module A codifier module arranges and organizes scenes extracted from a correlation analysis management module as shown in section 2. When a user gives some queries representing a condition, a context and a viewpoint, this module provides appropriate scene set dynamically by RDF. By these modules, we can obtain interrelationships between heterogeneous data by bridging the gap between general facts and specific concepts. For example, in the case of the space weather, a sensor data that shows abnormality of Dst index, which is one of the sensor data on the space weather related to Geomagnetic storm event, and an news article on interruption of relay broadcast for XVI Olympic Winter Games are interrelated in the viewpoint of “watching TV” while they are individually published from different communities. 7. Related Works The relationships among concepts are predefined on the basis of a bridge concept. Schema mappings [6] and bridge ontologies [7] are typically used for the bridge concept. These methods are employed to predefine the universal relationships between two different domains; however, it is quite difficult to understand these relationships in Figure 7. An implementation for interconnection of heterogeneous contests repositories applying to space weather data T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 34
- 49. most cases. As a result, conventional approaches can be employed only on a small scale. The QOM [8] realizes semi-automatic alignment of different ontologies quickly. However, there is no concern about contexts. That is, it is purpose to create static whole ontologies. The feature of our method is dynamic extraction of event-centric interrelationships depending on the content of web feeds selected by a user. The essences of our purpose are to dynamically select, integrate and operate various appropriate data resources depending on a context for distributed environment. Therefore, our method is important and effective to realize interconnection of the distributed heterogeneous data repositories. Recently, linked data [9] that connects various resources at the instance level have attracted attention. Especially, the Linking Open Data community project [10] tries to connect various RDF data. The project enables us to use a large number of open interlinked datasets as structured data. Some works extracts structured data from Wikipedia such as DBpedia [11] and YAGO [12]. These works provide static interlinks for RDF data. In near future, these interlinks apply to not only data but also device, environment, resources, etc. In this sense, it is difficult to expand various interlinks without excluding three uncertainties shown in section 1.1 because of heterogeneities of data-type, content and utilization purpose. Our system realizes dynamic interconnection among heterogeneous data resources by event-driven and event-centric computing with resolvers for uncertainties existing among those resources. Therefore, Our architecture can solve these problems. 8. Conclusion In this paper, we presented a three-layered system architecture for computing dynamic associations of events in nature to related knowledge resources. The important feature of our system is to realize dynamic interconnection among heterogeneous data resources by event-driven and event-centric commuting with resolvers for uncertainties existing among those resources. This realizes interconnection indirectly and dynamically by semantic units for the data of various types such as text data, multimedia data, sensor data etc. In other words, it navigates various appropriate data including data of heterogeneous data-type and heterogeneous fields depending on user's purpose and standpoint. In our current global environment, it is important to transmit significant knowledge to actual users from various data resources. In fact, most events affect various aspects of other areas, fields and communities. This helps a user to obtain related information on heterogeneous data-type, contents and fields while providing a wide understanding of the relationships between them depending on user's standpoint. As our future study, we will extend the system to peer-to-peer environment. We will also formulate the evaluation indexes of represented concepts and contents. Furthermore, we will apply our method to various fields and communities. References [1] Space Weather Information Center, NICT, http://swc.nict.go.jp/contents/. [2] National Space Weather Program Implementation Plan, 2nd Edition, FCM-P31-2000, Washington, DC, July 2000.Available in PDF at http://www.ofcm.gov/nswp-ip/tableofcontents.htm. T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 35
- 50. [3] K. Zettsu, T. Nakanishi, M. Iwazume, Y. Kidawara, Y. Kiyoki: Knowledge cluster systems for knowledge sharing, analysis and delivery among remote sites, Information Modelling and Knowledge Bases, vol. 19, pp. 282–289, 2008. [4] T. Nakanishi, K. Zettsu, K. Kidawara, Y. Kiyoki: A Context Dependent Dynamic Interconnection Method of Heterogeneous Knowledge Bases by Interrelation Management Function, In proceedings of the 19th European-Japanese Conference on Information Modelling and Knowledge Bases, Maribor, Slovenia, June, 2009. [5] K.-S. Kim, K. Zettsu, K. Kidawara, Y. Kiyoki: Moving Phenomenon: Aggregation and Analysis of Geotime-Tagged Contents on the Web, In proceedings of the 9th international symposium on Web Geographical Information Systems (W2GIS2009), pp.7-24, 2009. [6] R. J. Miller, L. M. Haas, M. A. Hernandez: Schema Mapping as Query Discovery, Proc. of the 26th International Conference on Very Large Data Bases (VLDB2000), pp. 77–88, 2000. [7] A. H. Doan, J. Madhavan, P. Domingos, A. Halevy: Learning to Map between Ontologies on the Semantic Web, Proc. of the 11th international conference on World Wide Web, pp. 662–673, 2002. [8] M. Ehrig, S.Staab: QOM–Quick Ontology Mapping, In Proc. of Third International Semantic Web Conference (ISWC 2004), pp. 683–697, Hiroshima, Japan (2004). [9] T. Berners-Lee, Linked Data, http://www.w3.org/DesignIssues/LinkedData.html, 2006. [10] Linking Open Data W3C SWEO Community Project, http://esw.w3.org/topic/SweoIG/TaskForces/CommunityProjects/LinkingOpenData/. [11] S. Auer, C. Bizer, J. Lehmann, G. Kobilarov, R. Cyganiak, Z. Ives: DBpedia: A Nucleus for a Web of Open Data, In proceedings of the 6th International and 2nd Asian Semantic Web Conference (ISWC2007+ASWC2007), pp.715-728, 2007. [12] F.M. Suchanek, G. Kansneci, G Weikum: YAGO: A Core of Semantic Knowledge Unifying WordNet and Wikipedia, In proceedings of the 16th international conference on World Wide Web, pp.697-706, 2007. T. Nakanishi et al. / A Three-Layered Architecture for Event-Centric Interconnections 36
- 51. Partial Updates in Complex-Value Databases Klaus-Dieter SCHEWE a,1 and Qing WANG b,2 a Software Competence Centre Hagenberg, Austria b University of Otago, Dunedin, New Zealand Abstract. Partial updates arise when a location bound to a complex value is up- dated in parallel. Compatibility of such partial updates to disjoint locations can be assured by applying applicative algebras. However, due to the arbitrary nesting of type constructors, locations of complex-value database are often defined at mul- tiple abstraction levels and thereby non-disjoint. Thus, applicative algebras is not as smooth as its simple definition suggests. In this paper, we investigate this prob- lem in the context of complex-value databases, where partial updates arise natu- rally in database transformations. We show that a more efficient solution can be ob- tained when generalising the notion of location and thus permitting dependencies between locations. On these grounds we develop a systematic approach to consis- tency checking for update sets that involve partial updates. Keywords. Abstract State Machine, partial update, complex value, applicative algebra, database transformation 1. Introduction According to Blass’s and Gurevich’s sequential and parallel ASM theses sequential3 and parallel algorithms are captured by sequential and general Abstract State Machines (ASMs), respectively [3,6] (see also [4]). A decisive characteristic of ASMs is that states are first-order structures consisting of updatable (partial) functions. Thus, in each step a set of locations is updated to new values, where a location is defined by an n-ary function symbol f in the (fixed) state signature of the ASM, and n values a1, . . . , an in the (fixed) base set B of the structures defining states. That is, in a state S the function symbol f is interpreted by a function fS : Bn → B, and an update of f(a1, . . . , an) to a new value b ∈ B gives rise to fS (a1, . . . , an) = b in the successor state S . The progression from a state S to a successor state S is defined by an update set Δ, i.e. a set of updates (, b) with a location and a new value b for this location, provided Δ is consistent, where consistency of an update set is defined by the uniqueness of new values for all locations, i.e. whenever (, b), (, b ) ∈ Δ hold, we must have b = b . However, this requirement is too strict, if the base set B contains values that themselves 1E-mail: kd.schewe@scch.at 2E-mail: qing.wang@otago.ac.nz 3In Gurevich’s seminal work “parallelism” actually means unbounded parallelism, whereas algorithms with an a priori given bound to parallelism in elementary computation steps are still considered to be sequential. Information Modelling and Knowledge Bases XXII A. Heimbürger et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-690-4-37 37
- 52. have a complex structure. For instance, if the values for a location are tuples (A1 : a1, . . . , Ak : ak), then updates to different attributes Ai and Aj can still be compatible. The same applies to lists, finite sets, counters, labelled ordered trees, etc., and is therefore of particular interest for database transformations over complex-value databases. It is therefore desirable to distinguish between total and partial updates. For the former ones consistency of an update set should remain unchanged, whereas for the latter ones we should strive to find a way to guarantee compatibility and then merge partial updates to a location in an update set into a single total update on . The problem of partial updates in ASMs was first observed by the research group on Foundations of Software Engineering at Microsoft Research during the development of the executable ASM specification language AsmL [7,8]. This motivated Gurevich’s and Tillmann’s investigation on the problem of partial updates over data types counter, set and map [9]. An algebraic framework was established by defining particles as unary operations over a datatype, and the parallel composition of particles as an abstraction of order-independent sequential composition. However, this fails to address partial updates over data types such as sequence as exemplified in [10]. This limitation led to the pro- posal of applicative algebras as a general solution to the problem of partial updates [11]. It was shown that the problem of partial updates over sequences and labeled ordered trees could be solved in this algebraic framework, and the approach in [9] was a special kind of an applicative algebra. Definition 1.1 An applicative algebra consists of elements, which comprise a trivial element ⊥ and a non-empty set denoted by a client type τ, a monoid of total unary operations (called particles) over the elements including a null particle λ, and a parallel composition operation Ω, which assigns a particle ΩM to each finite multiset M of particles, such that the following two conditions (AA1) and (AA2) are satisfied: (AA1) f(⊥) = ⊥ for each particle f, and λ(x) = ⊥ for every element x. (AA2) Ω{ {f} } = f, Ω(M { {id} }) = ΩM, and Ω(M { {λ} }) = λ. A multiset M of particles is called consistent iff ΩM = λ. When applying applicative algebras to the problem of partial updates each partial update (, b) has to be interpreted as a partical applied to the content of in state S (denoted by valS()) and all these particles form a multiset M that is aggregated to ΩM such that valS () = ΩM(valS()) holds, provided M is consistent. In this paper, we investigate the partial update problem in the context of complex- value databases. In database transformations, bounded parallelism is intrinsic and com- plex data structures form the core of each data model. Thus, the problem of partial updates arises naturally. Several examples of partial update problems encountered in complex-value database are provided in Section 2. Furthermore, in Section 2, we discuss the reasons why using applicative algebras is not as smooth as the simple definition above suggests. One of important assumptions of applicative algebra is that locations of partial updates must be disjoint. However, it is common in data models to permit the arbitrary nesting of complex-value constructors. Consequently, we need particles for each position in a complex value, and each nested structure requires its own parallel composition operation. It means that we have to deal with the theoretical possibility of infinitely many applicative algebras, which requires a K.-D. Schewe and Q. Wang / Partial Updates in Complex-Value Databases 38
- 53. mechanism for the construction of such algebras out of algebras for parts of the type of every object in a complex-value database. This leads to the question of how to efficiently check consistency for sets of partial updates. In view of these problems we propose an alternative solution to the problem of par- tial updates. The preliminaries such as the definition of partial locations, partial updates, and different kinds of dependencies among partial locations are handled in Section 3. We relax the disjointness assumption on the notion of location in order to reflect a natural and flexible computing environment for database computations. While in principle the prime locations bound to complex values are not independent from each other, we may consider each position within a complex value as a sublocation, which for simplicity of terminology we prefer to call also location. Then a partial update to a location is in fact a (partial) update to a sublocation. In doing so, we can transform the problems of consistency checking and parallel composition into two stages: normalisation of shared updates and integration of total updates, which are discussed in Section 4 and Section 5, correspondingly. The first stage deals with compatibility of operators in shared updates and the second one deals with compatibility of clusters of exclusive updates. The work in this paper is part of our research on formal foundations of database transformations. Taking an approach analogous to the ASM thesis we demonstrated that all database transformations are captured by a variant of Abstract State Machines [13]. Decisive for this work is the exploitation of meta-finite states [5] in order to capture the intrinsic finiteness of databases, the explicit use of background structures [2] to capture the requirements of data models, and the handling of genericity [1]. For XML database transformations the requirements for tree-based backgrounds were made explicit in [12], and a more convenient machine model called XML machines was developed permitting the use of monadic second-order logic. On these grounds we developed a logic to reason about database transformations [14]. 2. Motivation We begin with modifications on tuples in a relation since tuples represent a common view for locations in the relational model. As will be revealed in the following example, parallel manipulations on distinct attributes of a tuple are prohibited if only tuples are permissible locations in a state. Example 2.1 Let S be a state containing a nested relation schema R = {A1 : {A11 : D11, A12 : D22}, A2 : D2, A3 : D3} and a nested relation I(R) over R as shown in Figure 1 where oi (i = 1, 3) are tuple identifiers in I(R) and oij (j = 1, 2) are tuple identifers in the relations in the attribute A1 of tuples oi. Suppose that the following two rules execute in parallel, modifying values of attributes A2 and A3 of the same tuple. forall x, y, z with R(x, y, z) ∧ y = b3 do par R(x, y, z) := false R(x, y, c2) := true par enddo forall x, y, z with R(x, y, z) ∧ y = b3 do par R(x, y, z) := false R(x, b, z) := true par enddo K.-D. Schewe and Q. Wang / Partial Updates in Complex-Value Databases 39
- 54. A1 A2 A3 A11 A12 o1 o11 {(a11, a12), b c1 o12 (a 11, a12)} o3 o31 {(a31, a32)} b3 c3 Figure 1. A relation I(R) in nested relational databases The right rule changes the attribute value b3 in the second tuple to b, mean- while the left rule changes the attribute value c3 in the same tuple to c2. They yield pairs of updates {(R({(a31, a32)}, b, c3), true), (R({(a31, a32)}, b3, c3), false)} and {(R({[a31, a32)}, b3, c3), false), (R({(a31, a32)}, b3, c2), true)}, respectively. Since the rules are running in parallel, we get a set of updates, i.e., {(R({(a31, a32)}, b, c3), true), (R({(a31, a32)}, b3, c3), false), (R({(a31, a32)}, b3, c2), true)}. However, apply- ing such a set of updates results in replacing the tuple R({(a31, a32)}, b3, c3) by two tuples R({(a31, a32)}, b, c3), R({(a31, a32)}, b3, c2) rather than a single tuple R({(a31, a32)}, b, c2) as expected. A straightforward solution of solving this problem is to add a finite number of attribute functions as locations for accessing attributes of tuples. Thus, locations are extended to either an n-ary relational function symbol R with n arguments such as R(a1, ..., an), or a unary attribute function symbol with an argument in the form of fR.A1....Ak (o) for a relation name R, attributes A1, . . . , Ak and an identifier o. Note that, attribute functions cannot entirely replace relational functions. To delete a tuple from or add a tuple into a relation, we must still use relational functions. Attribute functions can only be used to modify the values of attributes, including NULL values. The following example illustrates how values of distinct attributes in the same tuple can be modified in parallel by using this approach. Example 2.2 Let us consider again the nested relation I(R) in Figure 1. Assume that there is a set of attribute functions with a one-to-one corresponding to the attributes in R, i.e., for each Ak ∈ {A1, A1.A11, A1.A12, A2, A3}, there is a fR.Ak (x) = y for a tuple identifier x in I(R) of a state S and a value y in the domain of Ak. Thus, we have the following locations and their interpretations for the second tuple of I(R). • valS(fR.A1 (o3)) = {(a31, a32)} • valS(fR.A2 (o3)) = b3 • valS(fR.A3 (o3)) = c3 • valS(fR.A1.A11 (o31)) = a31 • valS(fR.A1.A12 (o31)) = a32 • valS(fR .A1 (o3)(a31, a32)) = true • valS(R({(a31, a32)}, b3, c3)) = true Using this approach, the following rule is able to modify values of attributes A2 and A3 of the same tuple in parallel. forall x with R(x) ∧ fR.A2 (x) = b3 do par fR.A2 (x) := b K.-D. Schewe and Q. Wang / Partial Updates in Complex-Value Databases 40
- 55. Exploring the Variety of Random Documents with Different Content
- 56. People to be invited to the dramatic soirée of the Azure Society. We give six a year. No title is announced. Nobody except a committee of three knows even the name of the author of the play that is to be performed. Everything is kept a secret. Even the author doesn't know that his play has been chosen. Don't you think it's a delightful idea? ... An offspring of the New Thought! He agreed that it was a delightful idea. Shall I be invited? he asked. She answered gravely: I don't know. Are you going to play in it? She paused.... Yes. Then you must let me come. Talking of plays-- He stopped. He was on the edge of facetiously relating the episode of The Orient Pearl at Sir John Pilgrim's; but he withdrew in time. Suppose that The Orient Pearl was the piece to be performed by the Azure Society! It might well be. It was (in his opinion) just the sort of play that that sort of society would choose. Nevertheless he was as anxious as ever to see Elsie April act. He really thought that she could and would transfigure any play. Even his profound scorn of New Thought (a subject of which he was entirely ignorant) began to be modified--and by nothing but the enchantment of the tone in which Elsie April murmured the words, Azure Society! How soon is the performance? he demanded. Wednesday week, said she. That's the very day of my corner-stone-laying, he said. However, it doesn't matter. My little affair will be in the afternoon.
- 57. But it can't be, said she solemnly. It would interfere with us, and we should interfere with it. Our annual conference takes place in the afternoon. All London will be there. Said Mr. Marrier rather shamefaced: That's just it, Mr. Machin. It positively never occurred to me that the Azure Conference is to be on that very day. I never thought of it until nearly four o'clock. And then I scarcely knew how to explain it to you. I really don't know how it escaped me. Mr. Marrier's trouble was now out, and he had declined in Edward Henry's esteem. Mr. Marrier was afraid of him. Mr. Marrier's list of personages was no longer a miracle of foresight; it was a mere coincidence. He doubted if Mr. Marrier was worth even his three pounds a week. Edward Henry began to feel ruthless, Napoleonic. He was capable of brushing away the whole Azure Society and New Thought movement into limbo. You must please alter your date, said Elsie April. And she put her right elbow on the table and leaned her chin on it, and thus somehow established a domestic intimacy for the three amid all the blare and notoriety of the vast tea-room. Oh, but I can't! he said easily, familiarly. It was her occasional artichoke manner that had justified him in assuming this tone. I can't! he repeated. I've told Sir John I can't possibly be ready any earlier, and on the day after he'll almost certainly be on his way to Marseilles. Besides, I don't want to alter my date. My date is in the papers by this time. You've already done quite enough harm to the movement as it is, said Elsie April stoutly but ravishingly. Me--harm to the movement?
- 58. Haven't you stopped the building of our church? Oh! So you know Mr. Wrissell? Very well indeed. Anybody else would have done the same in my place, Edward Henry defended himself. Your cousin, Miss Euclid, would have done it, and Marrier here was in the affair with her. Ah! exclaimed Elsie April. But we didn't belong to the movement then! We didn't know.... Come now, Mr. Machin. Sir John Pilgrim will of course be a great show. But even if you've got him and manage to stick to him, we should beat you. You'll never get the audience you want if you don't change from Wednesday week. After all, the number of people who count in London is very small. And we've got nearly all of them. You've no idea-- I won't change from Wednesday week, said Edward Henry. This defiance of her put him into an extremely agitated felicity. Now, my dear Mr. Machin-- He was actually aware of the charm she was exerting, and yet he discovered that he could easily withstand it. Now, my dear Miss April, please don't try to take advantage of your beauty! She sat up. She was apparently measuring herself and him. Then you won't change the day, truly? Her urbanity was in no wise impaired. I won't, he laughed lightly. I dare say you aren't used to people like me, Miss April. (She might get the better of Seven Sachs, but not of him, Edward Henry Machin from the Five Towns!)
- 59. Marrier, said he suddenly, with a bluff humorous downrightness, you know you're in a very awkward position here, and you know you've got to see Alloyd for me before six o'clock. Be off with you. I will be responsible for Miss April. (I'll show these Londoners! he said to himself. It's simple enough when you once get into it.) And he did in fact succeed in dismissing Mr. Marrier, after the latter had talked Azure business with Miss April for a couple of minutes. I must go, too, said Elsie, imperturbable, impenetrable. One moment, he entreated, and masterfully signalled Marrier to depart. After all, he was paying the fellow three pounds a week. She watched Marrier thread his way out. Already she had put on her gloves. I must go, she repeated, her rich red lips then closed definitely. Have you a motor here? Edward Henry asked. No. Then, if I may, I'll see you home. You may, she said, gazing full at him. Whereby he was somewhat startled and put out of countenance. V. Are we friends? he asked roguishly. I hope so, she said, with no diminution of her inscrutability.
- 60. They were in a taxicab, rolling along the Embankment towards the Buckingham Palace Hotel, where she said she lived. He was happy. Why am I happy? he thought. What is there in her that makes me happy? He did not know. But he knew that he had never been in a taxicab, or anywhere else, with any woman half so elegant. Her elegance flattered him enormously. Here he was, a provincial man of business, ruffling it with the best of them! ... And she was young in her worldly maturity. Was she twenty-seven? She could not be more. She looked straight in front of her, faintly smiling.... Yes, he was fully aware that he was a married man. He had a distinct vision of the angelic Nellie, of the three children, and of his mother. But it seemed to him that his own case differed in some very subtle and yet effective manner from the similar case of any other married man. And he lived, unharassed by apprehensions, in the lively joy of the moment. But, she said, I hope you won't come to see me act. Why? Because I should prefer you not to. You would not be sympathetic to me. Oh, yes, I should. I shouldn't feel it so. And then with a swift disarrangement of all the folds of her skirt she turned and faced him. Mr. Machin, do you know why I've let you come with me? Because you're a good-natured woman, he said. She grew even graver, shaking her head. No! I simply wanted to tell you that you've ruined Rose, my cousin. Miss Euclid? Me ruined Miss Euclid?
- 61. Yes. You robbed her of her theatre--her one chance. He blushed. Excuse me, he said, I did no such thing. I simply bought her option from her. She was absolutely free to keep the option or let it go. The fact remains, said Elsie April, with humid eyes, the fact remains that she'd set her heart on having that theatre, and you failed her at the last instant. And she has nothing, and you've got the theatre entirely in your own hands. I'm not so silly as to suppose that you can't defend yourself legally. But let me tell you that Rose went to the United States heart-broken, and she's playing to empty houses there--empty houses! Whereas she might have been here in London, interested in her theatre, and preparing for a successful season. I'd no idea of this, breathed Edward Henry. He was dashed. I'm awfully sorry! Yes, no doubt. But there it is! Silence fell. He knew not what to say. He felt himself in one way innocent, but he felt himself in another way blackly guilty. His remorse for the telephone-trick which he had practised on Rose Euclid burst forth again after a long period of quiescence simulating death, and actually troubled him.... No, he was not guilty! He insisted in his heart that he was not guilty! And yet--and yet-- No taxicab ever travelled so quickly as that taxi-cab. Before he could gather together his forces it had arrived beneath the awning of the Buckingham Palace Hotel. His last words to her were: Now, I sha'nt change the day of my stone-laying. But don't worry about your conference. You know it'll be perfectly all right. He
- 62. spoke archly, with a brave attempt at cajolery; but in the recesses of his soul he was not sure that she had not defeated him in this their first encounter. However, Seven Sachs might talk as he chose--she was not such a persuasive creature as all that! She had scarcely even tried to be persuasive. At about a quarter-past six, when he saw his underling again, he said to Mr. Marrier: Marrier, I've got a great idea. We'll have that corner-stone- laying at night. After the theatres. Say half-past eleven. Torchlight! Fireworks from the cranes! It'll tickle old Pilgrim to death. I shall have a marquee with match-boarding sides fixed up inside, and heat it with a few of those smokeless stoves. We can easily lay on electricity. It will be absolutely the most sensational stone-laying that ever was. It'll be in all the papers all over the blessed world. Think of it! Torches! Fireworks from the cranes! ... But I won't change the day--neither for Miss April nor anybody else. Mr. Marrier dissolved in laudations. Well, Edward Henry agreed with false diffidence, it'll knock spots off some of 'em in this town! He felt that he had snatched victory out of defeat. But the next moment he was capable of feeling that Elsie April had defeated him even in his victory. Anyhow, she was a most disconcerting and fancy- monopolising creature. There was one source of unsullied gratification: he had shaved off his beard. VI.
- 63. Come up here, Sir John, Edward Henry called. You'll see better, and you'll be out of the crowd. And I'll show you something. He stood, in a fur coat, at the top of a short flight of rough- surfaced steps between two unplastered walls--a staircase which ultimately was to form part of an emergency exit from the dress- circle of the Regent Theatre. Sir John Pilgrim, also in a fur coat, stood near the bottom of the steps, with a glare of a Wells light full on him and throwing his shadow almost up to Edward Henry's feet. Around, Edward Henry could descry the vast mysterious forms of the building's skeleton--black in places, but in other places lit up by bright rays from the gaiety below, and showing glimpses of that gaiety in the occasional revelation of a woman's cloak through slits in the construction. High overhead, two gigantic cranes interlaced their arms; and even higher than the cranes, shone the stars of the clear spring night. The hour was nearly half-past twelve. The ceremony was concluded--and successfully concluded. All London had indeed been present. Half the aristocracy of England, and far more than half the aristocracy of the London stage! The entire preciosity of the metropolis! Journalists with influence enough to plunge the whole of Europe into war! In one short hour Edward Henry's right hand (peeping out from the superb fur coat which he had had the wit to buy) had made the acquaintance of scores upon scores of the most celebrated right hands in Britain. He had the sensation that in future, whenever he walked about the best streets of the West End, he would be continually compelled to stop and chat with august and renowned acquaintances, and that he would always be taking off his hat to fine ladies who flashed by nodding from powerful motor-cars.
- 64. Indeed, Edward Henry was surprised at the number of famous people who seemed to have nothing to do but attend advertising rituals at midnight or thereabouts. Sir John Pilgrim had, as Marrier predicted, attended to the advertisements. But Edward Henry had helped. And on the day itself the evening newspapers had taken the bit between their teeth and run off with the affair at a great pace. The affair was on all the contents-bills hours before it actually happened. Edward Henry had been interviewed several times, and had rather enjoyed that. Gradually he had perceived that his novel idea for a corner-stone-laying had caught the facile imagination of the London populace. For that night at least he was famous--as famous as anybody! Sir John had made a wondrous picturesque figure of himself as, in a raised corner of the crowded and beflagged marquee, he had flourished a trowel and talked about the great and enlightened public, and about the highest function of the drama, and about the duty of the artist to elevate, and about the solemn responsibility of theatrical managers, and about the absence of petty jealousies in the world of the stage. Everybody had vociferously applauded, while reporters turned rapidly the pages of their note-books. Ass! Edward Henry had said to himself with much force and sincerity,-- meaning Sir John,--but he too had vociferously applauded; for he was from the Five Towns, and in the Five Towns people are like that! Then Sir John had declared the corner-stone well and truly laid (it was on the corner which the electric sign of the future was destined to occupy), and, after being thanked, had wandered off shaking hands here and there absently, to arrive at length in the office of the
- 65. clerk of the works, where Edward Henry had arranged suitably to refresh the stone-layer and a few choice friends of both sexes. He had hoped that Elsie April would somehow reach that little office. But Elsie April was absent, indisposed. Her absence made the one blemish on the affair's perfection. Elsie April, it appeared, had been struck down by a cold which had entirely deprived her of her voice, so that the performance of the Azure Society's Dramatic Club, so eagerly anticipated by all London, had had to be postponed. Edward Henry bore the misfortune of the Azure Society with stoicism, but he had been extremely disappointed by the invisibility of Elsie April at his stone-laying. His eyes had wanted her. Sir John, awaking apparently out of a dream when Edward Henry had summoned him twice, climbed the uneven staircase and joined his host and youngest rival on the insecure planks and gangways that covered the first floor of the Regent Theatre. Come higher, said Edward Henry, mounting upward to the beginnings of the second story, above which hung suspended from the larger crane the great cage that was employed to carry brick and stone from the ground. The two fur coats almost mingled. Well, young man, said Sir John Pilgrim, your troubles will soon be beginning. Now Edward Henry hated to be addressed as young man, especially in the patronising tone which Sir John used. Moreover, he had a suspicion that in Sir John's mind was the illusion that Sir John alone was responsible for the creation of the Regent Theatre--that without Sir John's aid as a stone-layer it could never have existed.
- 66. You mean my troubles as a manager? said Edward Henry grimly. In twelve months from now, before I come back from my world's tour, you'll be ready to get rid of this thing on any terms. You will be wishing that you had imitated my example and kept out of Piccadilly Circus. Piccadilly Circus is sinister, my Alderman--sinister. Come up into the cage, Sir John, said Edward Henry. You'll get a still better view. Rather fine, isn't it, even from here? He climbed up into the cage and helped Sir John to climb. And, standing there in the immediate silence, Sir John murmured with emotion: We are alone with London! Edward Henry thought: Cuckoo! They heard footsteps resounding on loose planks in a distant corner. Who's there? Edward Henry called. Only me! replied a voice. Nobody takes any notice of me! Who is it? muttered Sir John. Alloyd, the architect, Edward Henry answered, and then calling loud: Come up here, Alloyd. The muffled and coated figure approached, hesitated, and then joined the other two in the cage. Let me introduce Mr. Alloyd, the architect--Sir John Pilgrim, said Edward Henry. Ah! said Sir John, bending towards Alloyd. Are you the genius who draws those amusing little lines and scrawls on transparent paper, Mr. Alloyd? Tell me, are they really necessary for a building, or
- 67. do you only do them for your own fun? Quite between ourselves, you know! I've often wondered. Said Mr. Alloyd with a pale smile: Of course everyone looks on the architect as a joke! The pause was somewhat difficult. You promised us rockets, Mr. Machin, said Sir John. My mind yearns for rockets. Right you are! Edward Henry complied. Close by, but somewhat above them, was the crane-engine, manned by an engineer whom Edward Henry was paying for overtime. A signal was given, and the cage containing the proprietor and the architect of the theatre and Sir John Pilgrim bounded most startlingly up into the air. Simultaneously it began to revolve rapidly on its cable, as such cages will, whether filled with bricks or with celebrities. Oh! ejaculated Sir John, terror-struck, clinging hard to the side of the cage. Oh! ejaculated Mr. Alloyd, also clinging hard. I want you to see London, said Edward Henry, who had been through the experience before. The wind blew cold above the chimneys. The cage came to a standstill exactly at the peak of the other crane. London lay beneath the trio. The curves of Regent Street and of Shaftesbury Avenue, the right lines of Piccadilly, Lower Regent Street, and Coventry Street, were displayed at their feet as on an illuminated map, over which crawled mannikins and toy autobuses. At their feet a long procession of automobiles were sliding off, one after another, with the guests of the evening. The metropolis stretched away, lifting to the north, and sinking to the south into
- 68. jewelled river on whose curved bank rose messages of light concerning whisky, tea, and beer. The peaceful nocturnal roar of the city, dwindling every moment now, reached them like an emanation from another world. You asked for a rocket, Sir John, said Edward Henry. You shall have it. He had taken a box of fuses from his pocket. He struck one, and his companions in the swaying cage now saw that a tremendous rocket was hung to the peak of the other crane. He lighted the fuse.... An instant of deathly suspense! ... And then with a terrific and a shattering bang and splutter the rocket shot towards the kingdom of heaven, and there burst into a vast dome of red blossoms which, irradiating a square mile of roofs, descended slowly and softly on the West End like a benediction. You always want crimson, don't you, Sir John? said Edward Henry, and the easy cheeriness of his voice gradually tranquillised the alarm natural to two very earthly men who for the first time found themselves suspended insecurely over a gulf. I have seen nothing so impressive since the Russian ballet, murmured Mr. Alloyd, recovering. You ought to go to Siberia, Alloyd, said Edward Henry. Sir John Pilgrim, pretending now to be extremely brave, suddenly turned on Edward Henry and in a convulsive grasp seized his hand. My friend, he said hoarsely, a thought has just occurred to me: you and I are the two most remarkable men in London! He glanced up as the cage trembled. How thin that steel rope seems! The cage slowly descended, with many twists.
- 69. Edward Henry said not a word. He was too deeply moved by his own triumph to be able to speak. Who else but me, he reflected, exultant, could have managed this affair as I've managed it? Did anyone else ever take Sir John Pilgrim up into the sky like a load of bricks, and frighten his life out of him? As the cage approached the platforms of the first story he saw two people waiting there; one he recognised as the faithful, harmless Marrier; the other was a woman. Someone here wants you urgently, Mr. Machin! cried Marrier. By Jove, exclaimed Alloyd under his breath, what a beautiful figure! No girl as attractive as that ever wanted me urgently! Some folks do have luck! The woman had moved a little away when the cage landed. Edward Henry followed her along the planking. It was Elsie April. I thought you were ill in bed, he breathed, astounded. Her answering voice reached him, scarcely audible: I'm only hoarse. My cousin Rose has arrived to-night in secret at Tilbury by the Minnetonka. The Minnetonka! he muttered. Staggering coincidence! Mystic heralding of misfortune! I was sent for, the pale ghost of a delicate voice continued. She's broken, ruined; no courage left. Awful fiasco in Chicago! She's hiding now at a little hotel in Soho. She absolutely declined to come to my hotel. I've done what I could for the moment. As I was driving by here just now I saw the rocket, and I thought of you. I thought you ought to know it. I thought it was my duty to tell you.
- 70. She held her muff to her mouth. She seemed to be trembling. A heavy hand was laid on his shoulder. Excuse me, sir, said a strong, rough voice. Are you the gent that fired off the rocket? It's against the law to do that kind o' thing here, and you ought to know it. I shall have to trouble you-- It was a policeman of the C division. Sir John was disappearing, with his stealthy and conspiratorial air, down the staircase.
- 71. CHAPTER VIII DEALING WITH ELSIE I. The headquarters of the Azure Society were situate in Marloes Road, for no other reason than that it happened so. Though certain famous people inhabit Marloes Road, no street could well be less fashionable than this thoroughfare, which is very arid and very long, and a very long way off the centre of the universe. The Azure Society, you know! Edward Henry added when he had given the exact address to the chauffeur of the taxi. The chauffeur, however, did not know, and did not seem to be ashamed of his ignorance. His attitude indicated that he despised Marloes Road, and was not particularly anxious for his vehicle to be seen therein, especially on a wet night, but that nevertheless he would endeavour to reach it. When he did reach it, and observed the large concourse of shining automobiles that struggled together in the rain in front of the illuminated number named by Edward Henry, the chauffeur admitted to himself that for once he had been mistaken, and his manner of receiving money from Edward Henry was generously respectful. Originally the headquarters of the Azure Society had been a seminary and schoolmistress' house. The thoroughness with which the buildings had been transformed showed that money was not among the things which the society had to search for. It had rich
- 72. resources, and it had also high social standing; and the deferential commissionaires at the doors and the fluffy-aproned, appealing girls who gave away programmes in the foyer were a proof that the society, while doubtless anxious about such subjects as the persistence of individuality after death, had no desire to reconstitute the community on a democratic basis. It was above such transient trifles of reform, and its high endeavours were confined to questions of immortality, of the infinite, of sex, and of art: which questions it discussed in fine raiment and with all the punctilio of courtly politeness. Edward Henry was late, in common with some two hundred other people of whom the majority were elegant women wearing Paris or almost Paris gowns with a difference. As on the current of the variegated throng he drifted through corridors into the bijou theatre of the society, he could not help feeling proud of his own presence there; and yet at the same time he was scorning, in his Five Towns way, the preciosity and the simperings of these his fellow creatures. Seated in the auditorium, at the end of a row, he was aware of an even keener satisfaction as people bowed and smiled at him; for the theatre was so tiny and the reunion so choice that it was obviously an honour and a distinction to have been invited to such an exclusive affair. To the evening first fixed for the dramatic soirée of the Azure Society he had received no invitation. But shortly after the postponement due to Elsie April's indisposition an envelope addressed by Marrier himself, and containing the sacred card, had arrived for him in Bursley. His instinct had been to ignore it, and for two days he had ignored it, and then he noticed in one corner the
- 73. initials E.A. Strange that it did not occur to him immediately that E.A. stood, or might stand, for Elsie April! Reflection brings wisdom and knowledge. In the end he was absolutely convinced that E.A. stood for Elsie April; and at the last moment, deciding that it would be the act of a fool and a coward to decline what was practically a personal request from a young and enchanting woman, he had come to London--short of sleep, it is true, owing to local convivialities, but he had come. And, curiously, he had not communicated with Marrier. Marrier had been extremely taken up with the dramatic soirée of the Azure Society, which Edward Henry justifiably but quite privately resented. Was he not paying three pounds a week to Marrier? And now, there he sat, known, watched, a notoriety, the card who had raised Pilgrim to the skies, probably the only theatrical proprietor in the crowded and silent audience; and he was expecting anxiously to see Elsie April again--across the footlights! He had not seen her since the night of the stone-laying, over a week earlier. He had not sought to see her. He had listened then to the delicate tones of her weak, whispering, thrilling voice, and had expressed regret for Rose Euclid's plight. But he had done no more. What could he have done? Clearly he could not have offered money to relieve the plight of Rose Euclid, who was the cousin of a girl as wealthy and as sympathetic as Elsie April. To do so would have been to insult Elsie. Yet he felt guilty none the less. An odd situation! The delicate tones of Elsie's weak, whispering, thrilling voice on the scaffolding haunted his memory, and came back with strange clearness as he sat waiting for the curtain to ascend.
- 74. There was an outburst of sedate applause, and a turning of heads to the right. Edward Henry looked in that direction. Rose Euclid herself was bowing from one of the two boxes on the first tier. Instantly she had been recognised and acknowledged, and the clapping had in nowise disturbed her. Evidently she accepted it as a matter of course. How famous, after all, she must be, if such an audience would pay her such a meed! She was pale, and dressed glitteringly in white. She seemed younger, more graceful, much more handsome, more in accordance with her renown. She was at home and at ease up there in the brightness of publicity. The imposing legend of her long career had survived the eclipse in the United States. Who could have guessed that some ten days before she had landed heart-broken and ruined at Tilbury from the Minnetonka? Edward Henry was impressed. She's none so dusty! he said to himself in the incomprehensible slang of the Five Towns. The phrase was a high compliment to Rose Euclid, aged fifty and looking anything you like over thirty. It measured the extent to which he was impressed. Yes, he felt guilty. He had to drop his eyes, lest hers should catch them. He examined guiltily the programme, which announced The New Don Juan, a play in three acts and in verse--author unnamed. The curtain went up. II. And with the rising of the curtain began Edward Henry's torture and bewilderment. The scene disclosed a cloth upon which was painted,
- 75. to the right, a vast writhing purple cuttlefish whose finer tentacles were lost above the proscenium-arch, and to the left an enormous crimson oblong patch with a hole in it. He referred to the programme, which said: Act. I. A castle in the forest, and also Scenery and costumes designed by Saracen Givington, A.R.A. The cuttlefish, then, was the purple forest, or perhaps one tree in the forest, and the oblong patch was the crimson castle. The stage remained empty, and Edward Henry had time to perceive that the footlights were unlit, and that rays came only from the flies and from the wings. He glanced round. Nobody had blenched. Quite confused, he referred again to the programme and deciphered in the increasing gloom, Lighting by Cosmo Clark, in very large letters. Two yellow-clad figures of no particular sex glided into view, and at the first words which they uttered Edward Henry's heart seemed in apprehension to cease to beat. A fear seized him. A few more words, and the fear became a positive assurance and realisation of evil. The New Don Juan was simply a pseudonym for Carlo Trent's Orient Pearl! ... He had always known that it would be. Ever since deciding to accept the invitation he had lived under just that menace. The Orient Pearl seemed to be pursuing him like a sinister destiny. Weakly he consulted yet again the programme. Only one character bore a name familiar to the Don Juan story; to wit, Haidee; and opposite that name was the name of Elsie April. He waited for her,--he had no other interest in the evening,--and he waited in resignation. A young female troubadour (styled in the programme the messenger) emerged from the unseen depths of
- 76. the forest in the wings and ejaculated to the hero and his friend: The woman appears. But it was not Elsie that appeared. Six times that troubadour messenger emerged and ejaculated, The woman appears, and each time Edward Henry was disappointed. But at the seventh heralding--the heralding of the seventh and highest heroine of this drama in hexameters--Elsie did at length appear. And Edward Henry became happy. He understood little more of the play than at the historic breakfast-party of Sir John Pilgrim; he was well confirmed in his belief that the play was exactly as preposterous as a play in verse must necessarily be; his manly contempt for verse was more firmly established than ever--but Elsie April made an exquisite figure between the castle and the forest; her voice did really set up physical vibrations in his spine. He was deliciously convinced that if she remained on the stage from everlasting to everlasting, just so long could he gaze thereat without surfeit and without other desire. The mischief was that she did not remain on the stage. With despair he saw her depart; and the close of the act was ashes in his mouth. The applause was tremendous. It was not as tremendous as that which had greeted the plate-smashing comedy at the Hanbridge Empire, but it was far more than sufficiently enthusiastic to startle and shock Edward Henry. In fact, his cold indifference was so conspicuous amid that fever, that in order to save his face he had to clap and to smile. And the dreadful thought crossed his mind, traversing it like the shudder of a distant earthquake that presages complete destruction: Are the ideas of the Five Towns all wrong? Am I a provincial after all?
- 77. For hitherto, though he had often admitted to himself that he was a provincial, he had never done so with sincerity; but always in a manner of playful and rather condescending badinage. III. Did you ever see such scenery and costumes? some one addressed him suddenly when the applause had died down. It was Mr. Alloyd, who had advanced up the aisle from the back row of the stalls. No, I never did! Edward Henry agreed. It's wonderful how Givington has managed to get away from the childish realism of the modern theatre, said Mr. Alloyd, without being ridiculous. You think so! said Edward Henry judicially. The question is, Has he? Do you mean it's too realistic for you? cried Mr. Alloyd. Well, you are advanced! I didn't know you were as anti-representational as all that! Neither did I! said Edward Henry. What do you think of the play? Well, answered Mr. Alloyd low and cautiously, with a somewhat shamed grin, between you and me, I think the play's bosh. Come, come! Edward Henry murmured as if in protest. The word bosh was almost the first word of the discussion which he had comprehended, and the honest familiar sound of it did him good. Nevertheless, keeping his presence of mind, he had
- 78. forborne to welcome it openly. He wondered what on earth anti- representational could mean. Similar conversations were proceeding around him, and each could be very closely heard, for the reason that, the audience being frankly intellectual and anxious to exchange ideas, the management had wisely avoided the expense and noise of an orchestra. The entr'acte was like a conversazione of all the cultures. I wish you'd give us some scenery and costumes like this in your theatre, said Alloyd as he strolled away. The remark stabbed him like a needle; the pain was gone in an instant, but it left a vague fear behind it, as of the menace of a mortal injury. It is a fact that Edward Henry blushed and grew gloomy, and he scarcely knew why. He looked about him timidly, half defiantly. A magnificently arrayed woman in the row in front, somewhat to the right, leaned back and towards him, and behind her fan said: You're the only manager here, Mr. Machin! How alive and alert you are! Her voice seemed to be charged with a hidden meaning. D'you think so? said Edward Henry. He had no idea who she might be. He had probably shaken hands with her at his stone- laying, but if so he had forgotten her face. He was fast becoming one of the oligarchical few who are recognised by far more people than they recognise. A beautiful play! said the woman. Not merely poetic, but intellectual. And an extraordinarily acute criticism of modern conditions! He nodded. What do you think of the scenery? he asked.
- 79. Well, of course candidly, said the woman, I think it's silly. I dare say I'm old-fashioned. I dare say, murmured Edward Henry. They told me you were very ironic, said she, flushing but meek. They! Who? Who in the world of London had been labelling him as ironic? He was rather proud. I hope if you do do this kind of play,--and we're all looking to you, Mr. Machin, said the lady making a new start,--I hope you won't go in for these costumes and scenery. That would never do! Again the stab of the needle! It wouldn't, he said. I'm delighted you think so, said she. An orange telegram came travelling from hand to hand along that row of stalls, and ultimately, after skipping a few persons, reached the magnificently arrayed woman, who read it and then passed it to Edward Henry. Splendid! she exclaimed. Splendid! Edward Henry read: Released. Isabel. What does it mean? It's from Isabel Joy--at Marseilles. Really! Edward Henry's ignorance of affairs round about the centre of the universe was occasionally distressing--to himself in particular. And just now he gravely blamed Mr. Marrier, who had neglected to post him about Isabel Joy. But how could Marrier honestly earn his three pounds a week if he was occupied night and day with the organising and management of these precious dramatic soirées?
- 80. Edward Henry decided that he must give Mr. Marrier a piece of his mind at the first opportunity. Don't you know? questioned the dame. How should I? he parried. I'm only a provincial. But surely, pursued the dame, you knew we'd sent her round the world. She started on the Kandahar, the ship that you stopped Sir John Pilgrim from taking. She almost atoned for his absence at Tilbury. Twenty-five reporters, anyway! Edward Henry sharply slapped his thigh, which in the Five Towns signifies, I shall forget my own name next. Of course! Isabel Joy was the advertising emissary of the Militant Suffragette Society, sent forth to hold a public meeting and make a speech in the principal ports of the world. She had guaranteed to circuit the globe and to be back in London within a hundred days, to speak in at least five languages, and to get herself arrested at least three times en route. Of course! Isabel Joy had possessed a very fair share of the newspapers on the day before the stone-laying, but Edward Henry had naturally had too many preoccupations to follow her exploits. After all, his momentary forgetfulness was rather excusable. She's made a superb beginning! said the resplendent dame, taking the telegram from Edward Henry and inducting it into another row. And before three months are out she'll be the talk of the entire earth. You'll see! Is everybody a suffragette here? asked Edward Henry simply, as his eyes witnessed the satisfaction spread by the voyaging telegram.
- 81. Practically, said the dame. These things always go hand in hand, she added in a deep tone. What things? the provincial demanded. But just then the curtain rose on the second act. IV. Won't you cam up to Miss April's dressing-room? said Mr. Marrier, who in the midst of the fulminating applause after the second act seemed to be inexplicably standing over him, having appeared in an instant out of nowhere like a genie. The fact was that Edward Henry had been gently and innocently dozing. It was in part the deep obscurity of the auditorium, in part his own physical fatigue, and in part the secret nature of poetry that had been responsible for this restful slumber. He had remained awake without difficulty during the first portion of the act, in which Elsie April--the orient pearl--had had a long scene of emotion and tears, played, as Edward Henry thought, magnificently in spite of its inherent ridiculousness; but later, when gentle Haidee had vanished away and the fateful troubadour messenger had begun to resume her announcements of The woman appears, Edward Henry's soul had miserably yielded to his body and to the temptation of darkness. The upturned lights and the ringing hosannahs had roused him to a full sense of sin, but he had not quite recovered all his faculties when Marrier startled him. Yes, yes! Of course! I was coming, he answered a little petulantly. But no petulance could impair the beaming optimism on
- 82. Mr. Marrier's features. To judge by those features, Mr. Marrier, in addition to having organised and managed the soirée, might also have written the piece and played every part in it, and founded the Azure Society and built its private theatre. The hour was Mr. Marrier's. Elsie April's dressing-room was small and very thickly populated, and the threshold of it was barred by eager persons who were half in and half out of the room. Through these Mr. Marrier's authority forced a way. The first man Edward Henry recognised in the tumult of bodies was Mr. Rollo Wrissell, whom he had not seen since their meeting at Slosson's. Mr. Wrissell, said the glowing Marrier, let me introduce Mr. Alderman Machin, of the Regent Theatah. Clumsy fool! thought Edward Henry, and stood as if entranced. But Mr. Wrissell held out a hand with the perfection of urbane insouciance. How d'you do, Mr. Machin? said he. I hope you'll forgive me for not having followed your advice. This was a lesson to Edward Henry. He learnt that you should never show a wound, and if possible never feel one. He admitted that in such details of social conduct London might be in advance of the Five Towns, despite the Five Towns' admirable downrightness. Lady Woldo was also in the dressing-room, glorious in black. Her beauty was positively disconcerting, and the more so on this occasion as she was bending over the faded Rose Euclid, who sat in a corner surrounded by a court. This court, comprising comparatively uncelebrated young women and men, listened with respect to the
- 83. conversation of the peeress (who called Rose my dear), the great star-actress, and the now somewhat notorious Five Towns character, Edward Henry Machin. Miss April is splendid, isn't she? said Edward Henry to Lady Woldo. Oh! My word, yes! replied Lady Woldo nicely, warmly, yet with a certain perfunctoriness. Edward Henry was astonished that everybody was not passionately enthusiastic about the charm of Elsie's performance. Then Lady Woldo added: But what a part for Miss Euclid! What a part for her! And there were murmurs of approbation. Rose Euclid gazed at Edward Henry palely and weakly. He considered her much less effective here than in her box. But her febrile gaze was effective enough to produce in him the needle-stab again, the feeling of gloom, of pessimism, of being gradually overtaken by an unseen and mysterious avenger. Yes, indeed! said he. He thought to himself: Now's the time for me to behave like Edward Henry Machin, and teach these people a thing or two! But he could not. A pretty young girl summoned all her forces to address the great proprietor of the Regent, to whom, however, she had not been introduced, and with a charming nervous earnest lisp said: But don't you think it's a great play, Mr. Machin? Of course! he replied, inwardly employing the most fearful and shocking anathemas. We were sure you would!
- 84. The young people glanced at each other with the satisfaction of proved prophets. D'you know that not another manager has taken the trouble to come here! said a second earnest young woman. Edward Henry's self-consciousness was now acute. He would have paid a ransom to be alone on a desert island in the Indian seas. He looked downwards, and noticed that all these bright eager persons, women and men, were wearing blue stockings or socks. Miss April is free now, said Marrier in his ear. The next instant he was talking alone to Elsie in another corner, while the rest of the room respectfully observed. So you deigned to come! said Elsie April. You did get my card! A little paint did her no harm, and the accentuation of her eyebrows and lips and the calculated disorder of her hair were not more than her powerful effulgent physique could stand. In a costume of green and silver she was magnificent, overwhelmingly magnificent. Her varying voice and her glance, at once sincere, timid, and bold, produced the most singular sensations behind Edward Henry's soft-frilled shirt-front. And he thought that he had never been through any experience so disturbing and so fine as just standing in front of her. I ought to be saying nice things to her, he reflected; but, no doubt because he had been born in the Five Towns, he could not formulate in his mind a single nice thing. Well, what do you think of it? she asked, looking full at him, and the glance too had a strange significance. It was as if she had
- 85. Welcome to our website – the perfect destination for book lovers and knowledge seekers. We believe that every book holds a new world, offering opportunities for learning, discovery, and personal growth. That’s why we are dedicated to bringing you a diverse collection of books, ranging from classic literature and specialized publications to self-development guides and children's books. More than just a book-buying platform, we strive to be a bridge connecting you with timeless cultural and intellectual values. With an elegant, user-friendly interface and a smart search system, you can quickly find the books that best suit your interests. Additionally, our special promotions and home delivery services help you save time and fully enjoy the joy of reading. Join us on a journey of knowledge exploration, passion nurturing, and personal growth every day! ebookbell.com