![The semantic relation between the first two proplets is intrapropositional functor-argument
structure, and is coded as follows: The first proplet with the core feature [noun: dog] specifies
the associated functor with the intrapropositional continuation feature [fnc: bark], while the
second proplet with the core feature [verb: bark] specifies its associated argument with [arg:
dog] (bidirectional pointering). That the first and the second proplet belong to the same
proposition is indicated by their having the same prn (proposition number) value, namely 22.
The semantic relation between the second and the third proplet is extrapropositional coor-
dination. That these two proplets belong to different propositions is indicated by their having
different prn values, namely 22 and 23, respectively. Their coordination relation is coded
in the second proplet by the extrapropositional continuation feature [nc: 23 run] and in the
third proplet by [pc: 22 bark], whereby the attributes nc and pc stand for “next conjunct” and
“previous conjunct,” respectively. The values of the nc and pc attributes are the proposition
number and the core value of the verb of the coordinated proposition.
By coding the semantic relations between proplets solely in terms of attributes and their
values, proplets can be stored and retrieved according to the needs of one’s database, without
any of the graphical restrictions induced by phrase structure trees. Furthermore, by using sim-
ilar proplet at the levels of language and context, the matching between the two levels during
language interpretation (hearer mode) and language production (speaker mode) is structurally
straightforward. Consider the following example in which the context level content of 3.2 is
matched with corresponding language proplets containing German surfaces:
3.3 MATCHING BETWEEN THE LANGUAGE AND THE CONTEXT LEVEL
sur: bellt
arg: dog
prn: 122
nc: 123 run
sur: fliehe
prn: 123
pc: 122 bark
arg: moi
sur: sur:
fnc: bark arg: dog
sur:
prn: 22 prn: 23
nc: 23 run pc: 22 bark
prn: 22
arg: moi
(horizontal relations)
(horizontal relations)
matching
internal (vertical relations)
sur: Hund
fnc: bark
prn: 122
noun:
verb: verb:
noun: verb:
dog
bark run
dog bark run
verb:
language level:
context level:
The proplets at the language and the context level are alike except that the sur (surface)
attributes of context proplets have an empty value, while those of the language proplets have
a language-dependent surface, e.g. Hund, as value.
On both levels, the intra- and extrapropositional relations are coded by means of attribute
values (horizontal relations, indicated by dotted lines). The reference relation between cor-
responding proplets at the two levels, in contrast, is based on matching (vertical relations,
indicated by double arrows). Simply speaking, the matching between a language and a con-
text proplet is successful if they have the same attributes and their values are compatible.
Even though the vertical matching takes place between individual proplets, the horizontal
semantic relations holding between the proplets at each of the two levels are taken into ac-
count as well. Assume, for example, that the noun proplet dog at the language level has the
fnc value bark, while the corresponding proplet at the context level had the fnc value sleep.
In this case, the two proplets would be vertically incompatible – due to their horizontal rela-
tions to different verbs, coded as different values of their respective fnc attributes.
Having described the data structure of Database Semantics, let us turn next to its algorithm.
For natural language communication, the time-linear algorithm of LA-grammar is used in
three different variants: (i) in the hearer mode, an LA-hear grammar interprets sentences of
natural language as sets of proplets ready to be stored in the database of the cognitive agent,
R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 7](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-23-320.jpg)
![Multi-Criterion Search from the
Semantic Point of View
(Comparing TIL and Description Logic)
Marie DUŽÍ,
VSB-Technical University Ostrava
17.listopadu 15
708 33 Ostrava
Czech Republic
Marie.Duzi@vsb.cz
Peter VOJTÁŠ
Charles University Prague
Malostranské námČstí 25
118 00 Praha 1
Czech Republic
Peter.Vojtas@mff.cuni.cz
Abstract In this paper we discuss two formal models apt for a search and
communication in a ‘multi-agent world’, namely TIL and EL@
. Specifying their
intersection, we are able to translate and switch between them. Using their union, we
extend their functionalities. The main asset of using TIL is a fine-grained rigorous
analysis and specification close to natural language. The additional contribution of EL@
consists in modelling multi-criterion aspects of user preferences. Using a simple
example throughout the paper, we illustrate the aspects of a multi-criterion search and
communication by their analysis and specification in both the systems. The paper is an
introductory study aiming at a universal logical approach to the ‘multi-agent world’,
which at the same time opens new research problems and trends.
1. Introduction and motivation.
In this paper we discuss two formal models that are relevant in the area of search and
communication in the multi-agent world, namely Transparent Intensional Logic (TIL) and a
fuzzy variant EL@
of the existential description logic EL (see [2]). Since TIL has been
introduced and discussed in the EJC proceedings and EL is a well-known logical system, we
are not going to introduce in details the technicalities of them. Instead, we provide just a
minimal necessary introduction to keep the paper self-contained and concentrate on the
analytic and specification role of these systems in the area of a semantic web search that takes
into account specific user fuzzy criteria. By comparing the two formalisms we aim at
providing a clue to their integration. Last but not least we’d like to illustrate the assets of a
rigorous logical approach to the problem.
The main asset of using TIL is a fine-grained rigorous analysis and specification close to
natural language. The additional contribution of EL@
consists in modelling multi-criterion
aspects of user preferences. The paper is an introductory study aiming at a universal logical
approach to the ‘multi-agent world’, which at the same time opens new research problems and
trends. The EL@
logic is a many-valued version of the existential description logic EL (see
[2]) where fuzzification concerns only concepts and the logic is enriched with aggregation
(see [21]). Specifying the intersection of TIL and EL@
, viz. the TIE@
L, we are able to translate
Information Modelling and Knowledge Bases XIX
H. Jaakkola et al. (Eds.)
IOS Press, 2008
© 2008 The authors and IOS Press. All rights reserved.
21](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-37-320.jpg)
![and switch between the two systems. Using their union, TI+E@
L, we extend their
functionalities. Throughout the paper we use a simple example in order to illustrate basic
principles, common features, as well as differences of the two systems.
Example Consider a simple communication between three agents, A, B and C. The agents can
be computational, like web services, database engines, query engines, pieces of software, or
even human ones. The agent A sends a message to B asking to find a hotel suitable for A (the
structure of the message and the meaning of ‘suitable’ will be discussed later). After obtaining
an answer the agent A chooses a hotel and sends another message to the agent C asking to
seek a suitable parking place close to the chosen hotel. The criteria of A are: hotel price (e.g.,
as low as possible), hotel distance to a beach (should be as close as possible), hotel year of
building (not too old), parking place price and parking place distance (to the hotel). We are
going to describe this scenario simultaneously in two formal models: TIL (Transparent
Intensional Logic) and DL (Description Logic).
Of course, the model can be made more realistic by considering a larger number of agents
searching for specific attribute values (this approach is motivated by Fagin in [10]). When
needed, we will switch between the levels of granularity in order to go into more details.
Using the DL and/or database notation we are thus going to consider agents of the type User,
and the attributes Hotel_Price, Hotel_Beach_Distance, Hotel_Year_of_Construction,
Parking_Price, Parking_Distance. Let the values of the attributes (results of the search) be:
Particular attribute preferences of a user U can be evaluated by assigning the preference
degree, a real number in the interval [0,1], to the attribute values. For instance, cheap_U(150)
= 0.75, close_U (300) = 0.6, new_U (1980) = 0.2, and similarly for the other values. In this
way we obtain fuzzy subsets cheap_U, close_U, new_U of the attribute domains, which can
be recorded in a fuzzy database operation table (see [15]):
Our reasoning and decision making is driven not only by the preferences we assign to the
values of attributes, but also by the weight we assign to the very criteria of interest. For
instance, when being short of money, the low price of the hotel is much more important than
its closeness to the beach. When being rich we may prefer a modern high-tech equipped hotel
situated on the beach. On the other hand a hotel close to the beach may become totally
unattractive in a tsunami-affected area. The multi-criterion decision is thus seldom based on a
simple conjunctive or disjunctive combination of the respective factors, and we need an
algorithm to compute global user preferences as a composition of particular weighted fuzzy
values of the selection criteria. The algorithm can be rather sophisticated. However, for the
sake of simplicity, let it be just a weighted average:
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View
22](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-38-320.jpg)
![6
_
_
3
_
2
)
_
,
_
,
(
@
U
new
U
close
U
cheap
U
new
U
close
U
cheap
U
Computing the global degree of preferences of the hotel h1 for the user U, we obtain:
...
58
.
0
6
5
.
3
6
2
.
0
6
.
0
3
75
.
0
2
)
2
.
0
,
6
.
0
,
75
.
0
(
@
U
Since this value is higher than the value of the hotel h2, the user U is going to choose h1. Of
course, another user can have different preferences, and also the preferences of one and the
same user may dynamically change in time.
Besides the fact that in a multi-agent world we work with vague, fuzzy or uncertain
information, we have to take into account also the demand on robustness and distribution of
the system. The system has to be fully distributive, and we have to deal with value gaps
because particular agents may fail to supply the requested data. On the other hand, in critical
and emergency situations, which tend to a chaotic behaviour, the need for an adequate data
becomes a crucial point. Therefore the classical systems which are based on the Closed World
Assumption are not plausible here. We have to work under the Open World Assumption
(OWA), and a lack of knowledge must not yield a collapse of the system.
For instance, it may happen that we are not able to retrieve the distance of the hotel h1 to the
beach, and the available data are as follows:
There are several possibilities of dealing with lacking data. We may use default values (e.g.,
average, the best or the worst ones), or treat the missing values as value gaps of partial
functions. From the formal point of view, TIL is a hyper-intensional partial O-calculus. By
‘hyper-intensional’ we mean the fact that the terms of the ‘language of TIL constructions’ are
not interpreted as the denoted functions, but as algorithmically structured procedures, known
as TIL constructions, producing the denoted functions as outputs. Thus we can rigorously and
naturally handle the terms that are in classical logics ‘non-denoting’, or undefined;1
in TIL
each term is denoting a full-right entity, namely a construction. Hence (well-typed) terms
never lack semantics. It may just happen (in well defined cases) that the denoted procedure
fails to produce an output function. And if it does not fail it may happen that the produced
function fails to have a value at an argument. These features of TIL are naturally combined
with and completed by the EL@
fuzzy tools, in particular the aggregation algorithms.
The paper is organized as follows: Chapter 2 contains brief introductory remarks on TIL.
Chapter 3 introduces the EL@
description logic, and Chapter 4 is devoted to the formal
description of our motivating examples, which gives us a flavour of the common features of
both the models. As a result, in concluding Chapter 5 we outline a possible hybrid system and
specify the trends of future research.
1
For the logic of definedness see [11].
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 23](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-39-320.jpg)
![2 TIL in brief.
In this Chapter we provide just a brief introductory explanation of the main notions of
Transparent Intensional Logic (TIL). For exact definitions and details see, e.g., [5], [7], [8],
[19], [20]. TIL approach to knowledge representation can be characterised as the ‘top-down
approach’. TIL ‘generalises to the hardest case’ and obtains the ‘less hard cases’ by lifting
various restrictions that apply only higher up. This way of proceeding is opposite to how
semantic theories tend to be built up. The standard approach consists in beginning with
atomic sentences, then proceeding to molecular sentences formed by means of truth-
functional connectives or by quantifiers, and from there to sentences containing modal
operators and, finally, attitudinal operators.
Thus, to use a simple case for illustration, once a vocabulary and rules of formation have been
laid down, a semantics gets off the ground by analysing an atomic sentence as follows:
(1) “Charles selected the hotel h”: S(a,h)
And further upwards:
(2) “Charles selected the hotel h, and Thelma is happy”: S(a,h) š H(b)
(3) “Somebody selected the hotel h”: x S(x,h)
(4) “Possibly, Charles selected the hotel h”: ‘ S(a,h)
(5) “Thelma believes that Charles selected the hotel h”: B(b,S(a,h)).
In non-hyperintensional (i.e., non-procedural) theories of formal semantics, attitudinal
operators are swallowed by the modal ones. But when they are not, we have three levels of
granularity: the coarse level of truth-values, the fine-grained level of truth-conditions
(propositions, truth-values-in-intension), and the very fine-grained level of hyper-
propositions, i.e., constructions of propositions. TIL operates with these three levels of
granularity. We start out by analysing sentences from the uppermost end, furnishing them
with a hyperintensional2
semantics, and working our way downwards, furnishing even the
lowest-end sentences (and other empirical expressions) with a hyperintensional semantics.
That is, the sense of a sentence such as “Charles selected the hotel h” is a hyper-proposition,
namely the construction of the denoted proposition (i.e., the instruction how to evaluate the
truth-conditions of the sentence in any state of affairs).
When assigning a construction to an expression as its meaning, we specify a procedural
know-how, which must not be confused with the respective performatory know-how.
Distinguishing performatory know-how from procedural know-how, the latter could be
characterised “that a knower x knows how A is done in the sense that x can spell out
instructions for doing A.”3
For instance, to know what Goldbach Conjecture means is to
understand the instruction to find whether ‘all positive even integers • 4 can be expressed as
the sum of two primes’. It does not include either actually finding out (whether it is true or not
by following a procedure or by luck) or possessing the skill to do so.4
Furthermore, the sentence “Charles selected the hotel h” is an ‘intensional context’, in the
sense that its logical analysis must involve reference to empirical parameters, in this case both
possible worlds and instants of time. Charles only contingently selected the hotel; i.e., he did
so only at some worlds and only sometimes. The other reason is because the analysans must
2
The term ‘hyperintensional’ has been introduced by Max Cresswell, see [4].
3
See [16, p.6]
4
For details on TIL handling knowledge see [8].
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View
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![Constructions that construct entities of order 1 are constructions of order 1. They belong to a
type of order 2, denoted by *1. This type *1 together with atomic types of order 1 serves as a
base for the induction rule: any collection of partial functions, 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 functions involving such constructions, belong to a type of
order 3. And so on ad infinitum.
Definition (Constructions)
i) Variables x, y, z, …are constructions that construct objects of the respective types
dependently on valuations v; they v-construct.
ii) Trivialization: Where X is an object whatsoever (an extension, an intension or a
construction), 0
X is a construction called trivialization. It constructs X without any
change.
iii) Composition: If X v-constructs a function F of a type (D E1…Em), and Y1,…,Ym v-construct
entities B1,…,Bm of types E1,…,Em, respectively, then the composition [X Y1 … Ym] is a
construction that v-constructs the value (an entity, if any, of type D) of the (partial)
function F on the argument ¢B1, …, Bn². Otherwise the composition [X Y1 … Ym] does not
v-construct anything: it is v-improper.
iv) Closure: If x1, x2, …,xm are pairwise distinct variables that v-construct entities of types E1,
E2, …, Em, respectively, and Y is a construction that v-constructs an entity of type D, then
[Ox1…xm Y] is a construction called closure, which v-constructs the following function F
of the type (D E1…Em), mapping E1 u…u Em to D: Let B1,…,Bm be entities of types
ȕ1,…,ȕm, respectively, and let v(B1/x1,…,Bm/xm) be a valuation differing from v at most in
associating the variables x1,…xm with B1,…,Bm, respectively. Then F associates with the
m-tuple ¢B1,…,Bm² the value v(B1/x1,…,Bm/xm)-constructed by Y. If Y is v(B1/x1,…,Bm/xm)-
improper (see iii), then F is undefined on ¢B1,…,Bm².
v) Double execution: If X is a construction that v-constructs a construction X’, then 2
X is a
construction called double execution. It v-constructs the entity (if any) v-constructed by
X’. Otherwise the double execution 2
X is v-improper.
vi) Nothing is a construction, unless it so follows from i) through vi).
The notion of construction is a notion that is the most misunderstood notion of those ones
used in TIL. Some logicians ask: Are constructions formulae of type-logic? Our answer: No!
Another question: Are they denotations of closed formulae? Our answer: No! So a pre-formal,
‘pre-theoretical’ characteristics is needed: constructions are abstract procedures. Question:
Procedures are time-consuming, how can they be abstract? Answer: The realization of an
algorithm is time-consuming, the algorithm itself is timeless and spaceless.
Question: So what about your symbolic language? Why do you not simply say that its
expressions are constructions? Answer: These expressions cannot construct anything they
serve only to represent (or encode) constructions.
Question: But you could do it like Montague6
did: To translate expressions of natural
language into the language of intensional logic, and then interpret the result in the standard
manner. What you achieve using ‘constructions’ you would get using metalanguage.
Answer(s):
First, Montague and other intensional logics interpret terms of their language as the respective
functions, i.e., set-theoretical mappings. However, these mappings are the outputs of
executing the respective procedures. Montague does not make it possible to mention the
6
For details on Montague system see, e.g., [12, pp. 117-220].
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View
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![procedures as objects sui generis, and to make thus a semantic shift to hyperintensions. Yet
we do need a hyperintensional semantics. Notoriously well-known are attitudinal sentences
which no intensional semantics can properly handle, because its finest individuation is
equivalence.7
Second, our logic is universal: we do not need to work as part-time
linguisticians. Using the ‘language of constructions’ we directly encode constructions.
Definition ((D-)intension, (D-)extension)
(D-)intensions are members of a type (DZ), i.e., functions from possible worlds to the
arbitrary type D. (D-)extensions are members of the type D, where D is not equal to (EZ) for
any E, i.e., extensions are not functions from possible worlds.
Remark on notational conventions: An object A of a type D is called an D-object, denoted
A/D. That a construction C v-constructs an D-object is denoted C ov D. We will often write
‘x A’, ‘x A’ instead of ‘[0
D
Ox A]’, ‘[0
D
Ox A]’, respectively, when no confusion can arise.
We also often use an infix notation without trivialisation when using constructions of truth-
value functions š (conjunction), › (disjunction), Š (implication), { (equivalence) and
negation (™), and when using a construction of an identity.
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). We will use variables w, w1, w2,… as v-constructing elements of type Z (possible
worlds), and t, t1, t2, … as v-constructing elements of type W (times). If C o DWZ v-constructs
an D-intension, the frequently used composition of a form [[C w] t], v-constructing the
intensional descent of the D-intension, will be abbreviated as Cwt.
Some important kinds of intensions are:
Propositions, type RWZ. They are denoted by empirical (declarative) sentences.
Properties of members of a type D, or simply Į-properties, type (RD)WZ.8
General terms (some
substantives, intransitive verbs) denote properties, mostly of individuals.
Relations-in-intension, type (RE1…Em)WZ. For example transitive empirical verbs, also
attitudinal verbs denote these relations. Omitting WZ we get the type (RE1…Em) of relations-in-
extension (to be met mainly in mathematics).
D-roles, offices, type DWZ, where D (RE). Frequently LWZ. Often denoted by concatenation of a
superlative and a noun (“the highest mountain”). Individual roles correspond to what Church
in [3] called “individual concept”.
The role of the above defined constructions in a communication between agents will be
illustrated in Chapter 4, in particular in Paragraph 4.5. Just a note to elucidate the role of
Trivialisation and empirical parameters w o Z, t o W: The TIL language is not based on a
fixed alphabet: the role of formal constants is here played by Trivialisations of non-
constructional entities, i.e., the atomic concepts of them. Each agent has to be equipped with a
basic ontology, namely the set of atomic concepts he knows. Thus the upper index ‘0
’ serves
as a marker of the atomic concept (like a ‘key-word’) that the agent should know. If they do
not, they have to learn it. The lower index ‘wt’ can be understood as an instruction to execute
an empirical inquiry (search) in order to obtain the actual current value of an intension, for
instance by searching agent’s database or by asking the other agents, or even by means of
agent’s sense perception.
7
See [12, p.73]
8
Collections, sets, classes of ‘D-objects’ are members of type (RD); TIL handles classes (subsets of a type) as
characteristic functions. Similarly relations (-in-extension) are of type(s) (Rȕ1…ȕm).
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 27](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-43-320.jpg)
![3 The EL@
description logic
In a multi-agent world like the semantic web we need to retrieve, process, share or reuse
information which is often vague or uncertain. The applications have to work with procedures
that deal with the degree of relatedness, similarity or ranking. These motivations lead to the
development of the fuzzy description logic (see, [18]). In this chapter we briefly describe a
variant of the fuzzy description logic, namely EL@
(see [21]).
One of the principal sources of fuzziness is user evaluation (preference) of crisp values of
attributes. For instance, the hotel price is crisp but user evaluation may lead to a fuzzy
predicate like a cheap, moderate, or expensive hotel. User preferences are modelled by
linearly ordered set of degrees T = [0,1] extending classical truth-values. Thus we have:
0 = False = A = the worst T
and
1 = True = T = the best T
Now when searching a suitable object we have to order the set of available objects according
to the user degrees assigned to object-attribute values. Practical experiences have shown that
the ordering is seldom based on a conjunctive or disjunctive combination of particular scores.
Rather, we need to work with a fuzzy aggregation function that combines generally
incomparable sets of values.
The EL@
logic is in some aspects a weakening of Straccia fuzzy description logic and in some
other aspects a strengthening.9
The restrictions concern using just crisp roles and not using
negation. Moreover, quantification is restricted to existential quantifiers. The extension
concerns the application of aggregation functions. Thus we loose the ability to describe
fuzziness in roles but gain the ability to compute a global user score.
The EL@
alphabet consists of (mutually disjoint) sets NC of concept names containing T, NR
role names, NI instance names and constructors containing and a finite set C of combination
functions with an arity function ar : C Æ {n N : n • 2}.
Concept descriptions in EL@
are formed according to the following syntax rules (where @C)
The interpretation structures of our description logic EL@
are parameterized by an ordered set
of truth-values T (the degrees of membership to a domain of a fuzzy concept) and a set of n-
ary aggregation functions over T. An interpretation structure T is thus an algebra
T = {T, •, {@•T: @ C }},
where (T , •,T ) is an upper complete semilattice with the top element T, and @•T: Tar(@)
Æ T
is a lattice of totally continuous (order-preserving) aggregation functions.
A T –interpretation is then a pair I = ¢ǻI
, •I
², with a nonempty domain ǻI
and the interpretation
of language elements
aI
ǻI
, for a NI
AI
: ǻI
Æ T, for A NC (concepts can be fuzzy, like a suitable hotel)
rI
Ž ǻI
× ǻI
, for r NR
9
For details on fuzzy description logic see [18].
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View
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![(Roles remain crisp; however, users may interpret these data in a fuzzy way. We
assume that fuzziness should not be attached to the data from the very beginning).
The extension of the T –interpretation I to the composed EL@
concepts is given by
(@(C1, …, Cn))I
(x) = @•(CI
1 (x), …, CI
n (x))
and
(r.C)I
(x) = sup{CI
(y): (x, y) rI
}
The EL@
is a surprisingly expressive language with good mathematical properties. It opens a
possibility to define declarative as well as procedural semantics of an answer to a user query
formulated by means of a fuzzy concept definition. The discussion on the complexity of
particular problems, like satisfiability, the instance problem, the problem of deciding
subsumption and the proof of soundness and completeness are, however, out of scope of the
present paper. For details, see, e.g., [21].
4 TIL and EL@
combined.
Using the example from the outset we are now going to outline the way of integrating the two
systems. We illustrate the work with a typed and / or non-typed language, and the role of
basic pre-concepts like a type, domain, concept and role. As stated above, TIL is a typed
system. The basic types serve as the pre-concepts.
4.1 Pre-concepts
a) Basic types
(TIL): The epistemic base is a collection of: R – the set of truth-values {T, F}, L – the
universe of discourse (the set of individuals), W – the set of times (temporal factor) and / or
real numbers, Z – the set of possible worlds (modal factor)
(EL@
): Basic pre-concepts are T and ǻI
, as specified in Chapter 3.
The description logic does not work explicitly with the temporal and modal factor. However,
there is a possibility to distinguish between necessary ex definitione (T-boxes) and
contingency of attribute values (A-boxes). Moreover, EL@
contributes the means for handling
user preference structures – the preference factor.
(TIL): The universe of discourse is the (universal) set of individuals.
EL@
works with varying domains of interpretation ǻI
.
b) Functions and relations
TIL is a functional system: Composed (functional) types are collections of partial functions;
D-sets and (DE)-relations are modelled by their characteristic functions, objects of types (RD),
(RDE), respectively.
(EL@
): Being a variant of description logic, EL@
is based on the first-order predicate logic
where n-ary predicates are interpreted as n-ary relations over the universe. However, in EL@
this is true only for n = 2: binary predicates are crisp roles. In the other aspects EL@
is
actually functional; it deals with (crisp) n-ary aggregation functions, and unary predicates
(concepts) are interpreted as fuzzy sets by their fuzzy characteristic functions ǻI
Æ T.
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 29](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-45-320.jpg)
![4.2 Assortment of the individuals in the universe
(TIL) properties
In order to classify individuals into particular sorts, we use properties of individuals. They are
intensions, namely functions that depending on the states of affairs (the modal parameter Z)
and time (the parameter W) yield a population of individuals (RL) that actually and currently
have the property in question.
Example: h1, h2, h3 / L are individuals with the property Hotel / (RL)WZ of being a hotel. In the
database setting these individuals belong to the domain of the attribute “hotel”, or, these
individuals may instantiate the entity set HOTEL. That h1, h2, h3 are hotels is in TIL
represented by the constructions of the respective propositions
OwOt [0
Hotelwt
0
h1], OwOt [0
Hotelwt
0
h2], OwOt [0
Hotelwt
0
h3],
where the property Hotel / (RL)WZ is first intensionally descended (0
Hotelwt) and then ascribed
to an individual: [0
Hotelwt
0
hi]. Finally, to complete the meaning of ‘hi is a hotel’, we have to
abstract over the modal and temporal parameter in order to construct a proposition of type RWZ
that hi is a hotel: OwOt [0
Hotelwt
0
hi].
Gloss the construction as an instruction for evaluating the truth-conditions: In any state of
affairs of evaluation (OwOt) check whether the individual (0
hi) currently belongs to the actual
population of hotels ([0
Hotelwt
0
hi]).
(EL@
) equivalents.
Names of properties correspond to the elements of NC and NR. The above propositions are
represented by membership assertions:
Hotel(h1), Hotel(h2), Hotel(h3).
The example continued. Let A, B, C / L are individuals with the property of being an agent. In
the database setting these individuals belong to the domain of the attribute “user”, or, these
individuals may instantiate the entity set AGENT. However, in order to be able to represent n-
ary properties of individuals by means of binary ones, we need to identify particular users. Of
course, in case of a big and varying set of users it is not in general possible to identify each
user, and we often have to consider (a smaller number of) user profiles.
(TIL): That A, B, C are agents is represented by the constructions of the respective
propositions:
OwOt [0
Agentwt
0
A], OwOt [0
Agentwt
0
B], OwOt [0
Agentwt
0
C],
where the property Agent / (RL)WZ is intensionally descended and then ascribed to an
individual: [0
Agentwt
0
Ai]. Finally, in order to construct a proposition, we have to abstract over
the parameters w, t: OwOt [0
Agentwt
0
Ai].
Gloss: In any state of affairs of evaluation check whether the individual A currently belongs to
the actual population of agents.
(EL@
): The above propositions are represented by membership assertions:
Agent(A), Agent(B), Agent(C).
(TIL): Parking / (RL)WZ; the property of an individual of being a parking place. For instance,
the proposition that p1, p2, …, pn / L are individuals with the property of being a parking
place, is constructed by
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View
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![OwOt [0
Parkingwt
0
pi].
(EL@
): These individuals belong to the extension of the concept:
Parking(pi).
4.3 Attributes – criteria
In general, attributes are empirical functions, i.e. intensions of a type (Įȕ)WZ. For instance, ‘the
President of (something)’ denotes a (singular) attribute. Dependently on the modal factor Z
and time W the function in question associates the respective country with the unique
individual playing the role of its President. But, for instance, George W. Bush might not have
been the President of the USA (the modal dependence), and he has not always been and will
soon not be10
the President (the temporal dependence).
(TIL) Price / (WL)WZ; an empirical function associating an individual (of type L) with a W-
number (its price); to obtain a price of a hotel hi, we have to execute an empirical procedure:
OwOt [0
Pricewt
0
hi].
(EL@
) the value of the attribute Price can be obtained, e.g., by an SQL query
SELECT Price FROM Hotel WHERE Hotel.Name=hi
or by using a crisp atomic role hotel_price.
(TIL) Distance / (WLL)WZ; an empirical function assigning a W-number (the distance) to a pair of
individuals, for instance: OwOt [0
Distancewt
0
hi
0
pi].
(TIL) DistE / (WL)WZ; the empirical function assigning to an individual a W-number (its distance
to another chosen entity E – a beach, a hotel, …).
(EL@
) Database point of view: Assuming we have a schema Distance(Source, Target, Value),
this is the value of the attribute Distance.Value. It can be obtained, e.g., by the SQL query
SELECT Distance.Value FROM Distance, Hotel WHERE Hotel.Name=hi AND
Hotel.Address=x AND Distance.Source=x AND Distance.Target=E
DL point of view: In DL we meet a problem here, because the relation Distance is of arity 3
and DL is a binary conceptual model. For each individual E we can consider an atomic role
hotel_distance_from_E. (Of course, in practical applications we can combine these
approaches).
(TIL) Year / (WL)WZ; an empirical function assigning to an individual a W-number (its year of
building).
(EL@
) Database and DL points of view similar as above
(TIL) Appertain-to / (R LL)WZ; the binary relation between individuals. For example, a parking
place pi belonging to a hotel hi:
OwOt [[0
Parkingwt
0
pi] š [0
Hotelwt
0
hi] š [0
Appertain-towt
0
hi
0
pi]].
(EL@
) the relation between a particular hotel and a parking; a crisp role
10
Written in January 2007
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 31](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-47-320.jpg)
![4.4 Evaluation of criteria by combining user preferences
The procedural semantics of TIL makes it possible to easily model the way particular agents
can learn by experience. An agent may begin with a small ontology of atomic primitive
concepts (trivialisations of entities) and gradually obtain pieces of information on more
detailed definitions of the entities. In TIL terminology each composed construction yielding
an entity E is an ontological definition of E. For instance, the agent A may specify the
property of being a Suitable (for-A) hotel by restricting the property Hotel. To this end the
property Suitable hotel is defined by the construction composing the price, distance and year
attribute values and yielding the degree greater than 0.5.
(TIL): Suitable-for / ((RL)WZ L (RL)WZ)WZ – an empirical (parameters W, Z) function that applied to
an individual (of type L) and a property (of type (RL)WZ) returns a property (of type (RL)WZ). For
instance, the property of being a suitable hotel for the agent A can be defined by:
OwOt [0
Suitable-forwt
0
A 0
Hotel] =
OwOt Ox [[0
Hotelwt x] š [[0
Evaluatewt
0
A [0
Pricewt x] [0
DistEwt x] [0
Yearwt x]] t 0.5]].
By way of further refining, we can again define the atomic concept 0
Evaluate. To this end we
enrich the ontology by 0
Aggregate and 0
Apt-for, which can again be refined. And so on,
theoretically ad infinitum.
Evaluate / (W L WWW)WZ - an empirical function that applied to an individual a and a triple of W-
parameters (e.g., price, distance, year) returns a W-number [0,1], which is the preference
degree of a particular hotel for the agent a.
[0
Evaluatewt a par1 par2 par3] =
[0
Aggregate [0
Apt-forwt a par1] [0
Apt-forwt a par2] [0
Apt-forwt a par3]].
Aggregate / (W WWW) – the aggregation function that applied to the triple of W-numbers
returns a W-number = the degree of appropriateness.
Apt-for / (W LW) – an empirical function that applied to an individual a / L and a W-
parameter pari (e.g., price, distance, and so like) returns a preference scale of the respective
parameter pari for the user a. The scale is a W-number [0,1].
For instance,
[0
Evaluatewt
0
A [0
Pricewt x] [0
DistEwt x] [0
Yearwt x]] = [0
Aggregate
[0
Apt-forwt A [0
Pricewt x]] [0
Apt-forwt A [0
DistEwt x]] [0
Apt-forwt A [0
Yearwt x]]].
The empirical function Evaluate is the key function here. Applied to an individual agent
(user) and particular criteria it returns the agent’s preference-degree of a particular object.
Each agent may dynamically (parameter W) choose (parameter Z) its own function Evaluate.
The algorithm computing the preference-degree of an object consists of two independent sub-
procedures:
i) user preference scale Apt-forwt of the TIL-type (W LW), or using the EL@
notation:
¢user, pari² o [0,1], where pari is the value of a particular criterion (for instance
price, distance, etc.).
Here the additional role of EL@
comes into play. The EL@
logic makes it possible to
choose an appropriate scale algorithm. It can be a specific function for a particular user
U1, e.g.:
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View
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![ii) the aggregation function Aggregate of the TIL -type (W WWW), or in the EL@
notation
(understood as a many valued connective) @: [0,1]3
o [0,1], computing the global
preference degree.
Here we consider the Aggregate function as not being user-dependent, but rather
system-dependent (therefore, in TIL –notation there is no WZ-parameter). In other words,
it is a system algorithm of computing the general user preference. Of course, we might
let each user specify his/her/its own algorithm but in practice it suffices to consider
different user profiles associated with each aggregation function. Thus the system may
test several algorithms of aggregation, e.g., those that were used for users with a similar
profile, in order to choose the suitable aggregation. It does not seem to be necessary to
further refine the specification in TIL. Instead we either call at this point a software
module, or make use of the EL@
logic. In the example above we used the weighted
average:
4.5 Communication of agents; messages
The communication aspects are not elaborated in EL@
from the semantic point of view. Hence
it represents the added value of TIL when integrating with EL@
. However, in SQL we have
ORDER BY command and when dealing with preferences we work with the notion of the
best, top-k, respectively, answers. The EL@
many valued logic setting understood as a
comparative tool (numerical values do not matter) is an appropriate tool for evaluating fuzzy
predicates. It provides a good semantics for ordering preferences of answers (see [13]).
The TIL-philosophy is driven by the fact that natural language is a perfect logical language.
Hence the TIL-specification is close to an ordinary human reasoning and natural-language
communication. On the other hand, however, the high expressive power of the TIL language
of constructions may sometimes be an obstacle to an effective implementation. This problem
is dealt with by the step-by-step refinement as discussed above. At the first step we specify
just a coarse-grained logical form of a message; the execution is left to particular Java
modules. Then a more fine-grained specification makes it possible to increase agent’s
“intelligence” by letting him dynamically decide which finer software modules should be
called. To this end we combine Java modules, Prolog, fuzzy Prolog Ciao, etc.
(TIL): The general scheme of a message is:
Message / (R L L RWZ)WZ
OwOt [0
Messagewt
0
Who 0
Whom OwOt [0
Typewt
0
What]],
where
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 33](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-49-320.jpg)
![Who /L, Whom /L, What (content)/ĮWZ, Type / (RĮWZ)WZ,
What – the subject of the message is a specification of an intension (usually a
proposition of type RWZ).
(EL@
): The description logic does not incorporate a specific semantic logical description of
messages. It is usually handled by an implementation component (generally in the Software
Engineering part) by dealing with exceptions, deadlocks, etc.
(TIL): There are three basic types of messages that concern propositions; i.e., these types are
properties of propositions, namely Order, Inform, Query/(RRWZ)WZ. In an ordinary
communication act we implicitly use the type Inform affirming that the respective proposition
is true. But using an interrogative sentence we ask whether the proposition is true (Query), or
using an imperative sentence we wish that the proposition were true (Order).
The content of a message is then the construction of a proposition, the scheme of which is
given by:
OwOt [0
Typewt
0
What] o RWZ.
In what follows we specify in more details possible typical types of messages.
Type = {Seek, Query(Yes-No), Answer, Order, Inform, Unrecognised, Refine,…}; where
Typei / (RDWZ)WZ or Typei / (R n)WZ.
Examples of a content of a message:
[0
Seekwt
0
What]; What / DWZ o send me an answer = the actual D-value of What in a
given state of affairs w,t of evaluation.
[0
Querywt
0
What]; What / RWZ o send me an answer = the actual R-truth-value of What
in a given state of affairs w,t.
[0
Orderwt
0
What]; What / RWZ o manage What to be actually True (in a state of affairs
w,t.)
[0
Informwt
0
What]; What / RWZ o informing that What is actually True
[[0
Answerwt
0
What] = a / D]; where a = [0
Whatwt]; the answer to a preceding query or
seek.
[0
Unrecognisedwt
00
What]; the atomic concept 0
What has not been recognised; a request
for refinement.
Note that Unrecognised is of type (R n)WZ, the property of a construction (usually
an atomic concept). Therefore the content of the message is not the intension
What constructed by 0
What, but the construction 0
What itself. The latter is
mentioned here by trivialisation, therefore 00
What.
[[0
Refinewt
00
What] = 0
C o DWZ]; an answer to the message on unrecognised atomic
concept. The construction C is the respective composed specification (definition)
of What, i.e., C and 0
What are equivalent, they construct the same entity:
C = 0
What.
For instance, the set of prime numbers can be defined as the set of numbers with
two factors: [[0
Refinewt
00
Prime] = 0
[Ox [0
Card Oy [0
Div x y] = 0
2]]], where
x, y o Nat (the type of natural numbers), Div / (R Nat Nat) – the relation of
being divisible by, Card / (Nat (R Nat))– the number of elements of a set.
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View
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![4.6 Example of communication
Now we continue the simple example from the outset. We will analyse a part of the dialog of
the three agents A, B, C. Sentences will be first written in ordinary English then analysed
using TIL, transformed into the standardised message, and if needed provided by a gloss. For
the sake of simplicity we will omit the specification of TIL-types of particular objects
contained in a message. However, since the TIL-type is an inseparable part of the respective
TIL-construction, we do not omit it in a real communication of agents. For instance, when
building an agent’s ontology, each concept is inserted with its typing.
Message 1 (A to B): ‘I wish B to seek a suitable hotel for me.’
A(TIL): OwOt [0
Wishwt
0
A OwOt [0
Seekwt
0
B [0
Suitable-forwt
0
A 0
Hotel]]],
Wish/(RLRWZ)WZ, Seek/(RL(RL)WZ)WZ,
A(TIL m1): OwOt [0
Messagewt
0
A 0
B OwOt [0
Seekwt [0
Suitable-forwt
0
A 0
Hotel]]]
Gloss: The agent A is sending a message to B asking to seek a suitable hotel for A.
Message 2 (B to A):
However, the agent B does not understand the sub-instruction [0
Suitable-forwt
0
A 0
Hotel],
because he does not have the atomic concept 0
Suitable-for in his ontology. Therefore, he
replies a message to A, asking to explain:
‘I did not recognise 0
Suitable-for.’
B(TIL m2): OwOt [0
Messagewt
0
B 0
A OwOt [0
Unrecognisedwt
00
Suitable-for]
Remark Thus the lower index wt can be understood as an instruction to execute an empirical
inquiry (search) in order to obtain the actual current value of an intension, here the property
of being a suitable hotel (for instance by searching agent’s database or by asking the other
agents, or even by means of agent’s sense perception).
The upper index 0
serves as a marker of the primitive (atomic) concept belonging the agent’s
ontology. If it does not, i.e., if the agent does not know the concept, he has to ask the others in
order to learn by experience.
Message 3 (A to B):
The agent A replies by specifying the restriction of the property Hotel to those hotels which
are evaluated with respect to price, distance and the year of building with the degree higher
than 0.5:
A(TIL) 0
Suitable-for / ((RL)WZ L (RL)WZ)WZ, a o L, p o (RL)WZ;
0
Suitable-for = OwOt Oap
OwOt Ox [[pwt x] š [[0
Evaluateh
wt a [0
Pricewt x] [0
DistEwt x] [0
Yearwt x]] t 0
0.5]].
Gloss: The A’s answer message should refine the atomic concept 0
Suitable-for. Now there is a
problem, however. The agent B would have to remember the respective message asking for
the refinement in order to apply the property to proper arguments (namely A and Hotel). This
would not be plausible in practice, because A is the aid prayer, not B. Therefore the answer
message contains the smallest constituent containing the refined concept:
A(TIL m3): OwOt [0
Messagewt
0
A 0
B OwOt [0
Refinewt
0
[0
Suitable-forwt
0
A 0
Hotel] =
0
[OwOt Ox [[0
Hotelwt x] š [[0
Evaluateh
wt
0
A [0
Pricewt x] [0
DistEwt x] [0
Yearwt x]] t 0.5]]]]]
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 35](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-51-320.jpg)
![In this way the agent B obtains a piece of knowledge what should he look for. Another
possibility would be A’s sending the original message 1 refined, i.e., the constituent
[0
Suitable-forwt
0
A 0
Hotel] replaced by the new specification:
A(TIL m3’): OwOt [0
Messagewt
0
A 0
B OwOt [0
Seekwt
OwOt Ox [[0
Hotelwt x] š [[0
Evaluateh
wt
0
A [0
Pricewt x] [0
DistEwt x] [0
Yearwt x]] t 0.5]]]]
However, we prefer the former, because in this way B learned what a suitable hotel for A
means. Or rather, he would learn if he understood 0
Evaluateh
, which may not be the case if he
received the request for the first time. Thus if B does not have the concept in his /her
ontology, he again sends a message asking for explaining:
Message 4 (B to A):
B: I did not recognise 0
Evaluateh
.
B(TIL m4): OwOt [0
Messagewt
0
B 0
A OwOt [0
Unrecognisedwt
00
Evaluateh
]
Message 5 (A to B):
A(TIL m5): OwOt [0
Messagewt
0
A 0
B OwOt [0
Refinewt
0
[0
Evaluatewt
0
A [0
Pricewt x] [0
DistEwt x] [0
Yearwt x]] =
= 0
[0
Aggregate [0
Apt-forwt A [0
Pricewt x]] [0
Apt-forwt A [0
DistEwt x]] [0
Apt-forwt A [0
Yearwt x]]]
And so on, the refinement may continue and the agents may learn new concepts (from the
theoretical point of view ad infinitum).
Anyway, finally B fully understands the message and attempts at fulfilling the task; recall that
he is to seek a suitable hotel for A.
Note that the whole process is dynamic, even agents’ learning by the process of refining
particular atomic concepts. B knows now that actually and currently a hotel suitable for A is
such a hotel the price, distance from the beach and the year of building of which evaluate with
respect to A’s scaling [0
Apt-forwt
0
A] with the degree higher than 0.5. But he also knows that it
might have been otherwise (the modal parameter w / Z) and it will not have to be always so
(the temporal parameter t / W). In other words, A and B now share common knowledge of the
composed concept defining the property of being a suitable hotel for A.
When eventually B accomplishes his search he sends an answer to A:
Message 6 (B to A):
A(TIL m6): OwOt [0
Messagewt
0
B 0
A OwOt [0
Answerwt [0
Suitable-forwt
0
A 0
Hotel] =
{¢h1,0.7²,{¢h5,0.53²}] 11
Gloss: B found out that there are two instances of the property v-constructed by the
construction [0
Suitable-forwt
0
A 0
Hotel], namely the hotel h1 that has been evaluated with the
degree 0.7 and h5 with the degree 0.53.
Since h1 has been evaluated as better than h5, A chooses the former.
At this point the communication can continue as a dialogue between A and C in a similar way
as above. The aim is now finding a suitable parking close to the chosen hotel h1 and then
asking to navigate to the chosen parking place:
OwOt [0
Messagewt
0
A 0
C OwOt [0
Seekwt [0
Suitablep
wt
0
A 0
Parking]]]
11
Here we use the classical set-theoretic notation without trivialisation, for the sake of simplicity.
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View
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![OwOt [0
Messagewt
0
C 0
A OwOt [0
Unrecognisedwt
00
Suitablep
]
OwOt [0
Messagewt
0
A 0
C OwOt [0
Refinewt
0
[0
Suitablep
wt
0
A 0
Parking] =
0
[OwOt Ox [[0
Parkingwt x] š [[0
Evaluatep
wt
0
A [0
Pricewt x] [0
DistEwt x]] t 0
0.5]]]]]
OwOt [0
Messagewt
0
C 0
A OwOt [0
Answerwt [0
Suitablep
wt
0
A 0
Parking]] =
{{p2,0.93},{p1,0.53}]
The message closing the dialogue might be sent from A to C:
OwOt [0
Messagewt
0
A 0
C OwOt [0
Orderwt OwOt [0
Navigate-towt
0
p2]]].
At this point the agent C must have 0
Navigate-to in his/her ontology (if he/she does not then
the learning process described above begins); C thus knows that he/she has to call another
agent D which is a GIS-agent that provides navigation facilities (see [6]).
Concluding this paragraph we again compare the TIL approach with EL@
. An analogy to the
above described means of communication can be found in the DL community. There are
heuristics for the top-k search (see [13]). However, these facilities lack any formal / logic /
semantic specification. The development of description logic and its variants can be
considered as a step forward to the development of languages which extend W3C standards.
In [9] a step in this direction is described. In particular the EL@
variant of the description logic
can be embedded into classical two-valued description logic with concrete domains (see [1]),
and thus also into OWL (or a slight extension of it). Using the results described in this paper,
especially the added value of TIL, we can expect the extension of W3C based specification of
web service languages using the OWL representation.
5. Conclusion: A hybrid system
In the previous chapters, especially by using the parallel description of our motivating
example in Chapter 4, we tried to show that TIL and EL@
have many features in common.
Both the systems can share some basic types, functions, concepts and roles; both the systems
distinguish extensional and intentional context (the former being modelled by the intensional
descent in TIL and A-Boxes in DL, the latter illustrated here by the (user-) definition or
specification of a multi-criterion search). These features can form the intersection TIE@L. On
the other hand, both the systems can be enhanced by accommodating features of the other
system, thus forming a union TI+E@L. The main contribution of EL@
is the method of
modelling multi-criterion aspects of user preferences (some heuristics have been tested in
separate works), and computing global user preferences by means of the aggregation
functions and scaling. TIL contributes to this union the method of a very fine-grained and
rigorous knowledge specification closed to natural language, including procedural hyper-
intensional semantics. We are convinced that these aspects are crucial for a smooth
communication and reasoning of agents in the multi-agent world. Artificial Intelligence is
sometimes characterised as a ‘struggle for consistency’. To put it slightly metaphorically,
reality is consistent. Only our ‘making it explicit’ in language may lead to paradoxes and
inconsistencies due to misinterpretations that are caused by a too coarse-grained analysis of
assumptions.
The specification of the formal model of the hybrid system is however still a subject of further
research. Currently we plan to perform experiments and tests on real data using the hints
described in Chapter 4.
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 37](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-53-320.jpg)
![In the team led by M. Duží, working on the project “Logic and Artificial Intelligence for
multi-agent systems” (see http://labis.vsb.cz/), we pursue research on multi-agent systems
based on TIL. Currently we implemented software modules simulating the behaviour of
mobile agents in a traffic system. The agents can choose particular realisations of their pre-
defined processes; moreover, they are able to dynamically adjust their behaviour dependently
on changing states of affairs in the environment. They communicate by message-exchange
system. To this end the TIL-Script language (see [14]) has been designed and it is currently
being implemented. We also plan to test some modules with EL@
features.
The project in which P. Vojtas is involved (see [17]) deals with theoretical models compatible
with W3C standards and experimental testing of multi-criterion search dependent on user
preferences. We believe that the TIL features will enhance the system with a rigorous
semantic description and specification of the software / implementation parts.
When pursuing the research we soon came to the conclusion that the area of the semantic web
and multi-agent world in general is so broad that it is almost impossible to create a universal
development method. Instead we decided to develop a methodology comprising and
integrating particular existing and/or newly developed methods as well as our fine-grained
rigorous logic. The paper is an introductory study aiming at a more universal logical approach
to the ‘multi-agent world’, which at the same time opens new research problems and trends.
The main challenges are formal measures (soundness and completeness) and implementation
measures of the integrated hybrid system.
––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
ACKNOWLEDGEMENTS
This work has been supported by the project No. 1ET101940420 “Logic and Artificial Intelligence for multi-
agent systems” within the program “Information Society” of the Czech Academy of Sciences, and by the
“Semantic Web” project No. 1ET100300419 of the Czech IT agency.
REFERENCES
[1] Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. eds. (2002): Description
Logic Handbook, Cambridge University Press.
[2] Brandt, S. (2004): Polynomial Time Reasoning in a Description Logic with Existential Restrictions, GCI
Axioms, and What Else? In R. López de Mantáras et al. eds. In Proc. ECAI-2004, pp. 298-302. IOS Press.
[3] Church, A. (1956): Introduction to Mathematical Logic I. Princeton.
[4] Cresswell, M.J. (1985): Structured meanings. MIT Press, Cambridge, Mass.
[5] Duží, M.(2004): Concepts, Language and Ontologies (from the logical point of view). In Information
Modelling and Knowledge Bases XV. Ed. Y. Kiyoki, H. Kangassalo, E Kawaguchi, IOS Press Amsterdam,
Vol. XV, 193-209.
[6] Duží, M., Ćuráková, D., DČrgel, P., Gajdoš, P., Müller, J. (2007): Logic Artificial Inteligence for Multi-
Agent Systems. In Information Modelling and Knowledge Bases XVIII. M. Duží, H. Jaakkola, Y. Kyioki,
H.Kangassalo (Eds.), IOS Press Amsterdam, 236-244.
[7] Duží, M., Heimburger A. (2006): Web Ontology Languages: Theory and practice, will they ever meet?. In
Information Modelling and Knowledge Bases XVII. Ed. Y. Kiyoki, J. Henno, H. Jaakkola, H. Kangassalo,
IOS Press Amsterdam, Vol. XVII, 20-37.
[8] Duží, M., Jespersen B, Müller, J. (2005): Epistemic Closure and Inferable Knowledge. In the Logica
Yearbook 2004. Ed. Libor BČhounek, Marta Bílková, Filosofia Praha, Vol. 2004, 1-15.
[9] Eckhardt, A., Pokorný, J., Vojtáš, P. (2006): Integrating user and group preferences for top-k search from
distributed web resources, technical report 2006
[10] Fagin, R. (1999): Combining fuzzy information from multiple systems, Journal of Comput. System Sci. 58,
1999, 83-99
[11] Feferman, S. (1995): ‘Definedness’. Erkenntnis 43, pp. 295-320.
[12] Gamut, L.T.F. (1991): Logic, Language and Meaning. Volume II. Intensional Logic and Logical Grammar.
M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View
38](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-54-320.jpg)
![That fling at our devoted army would have served as a clarion call to
us—had any been needed—to remember the absent.
“It will be a blunder in us not to overlook that blunder of General
Shepley’s,” urged Uncle Randolph.[1] “The important point is that the
policy of conciliation is to be pursued.” With the “Whig” in his hand,
Uncle Randolph told Matoaca that the Thursday before Virginia
seceded a procession of prominent Virginians marched up Franklin
Street, carrying the flag of the Union and singing “Columbia,” and
that he was with them.
The family questioned if his mind were wandering, when he went
on: “The breach can be healed—in spite of the bloodshed—if only
the Government will pursue the right course now. Both sides are
tired of hating and being hated, killing and being killed—this war
between brothers—if Weitzel’s orders reflect the mind of Lincoln and
Grant—and they must—all may be well—before so very long.”
These were the men of the Union Army who saved Richmond: The
First Brigade, Third Division (Deven’s Division), Twenty-fourth Army
Corps, Army of the James, Brevet-Brigadier-General Edward H.
Ripley commanding. This brigade was composed of the Eleventh
Connecticut, Thirteenth New Hampshire, Nineteenth Wisconsin,
Eighty-first New York, Ninety-eighth New York, One Hundredth and
Thirty-ninth New York, Convalescent detachment from the second
and third divisions of Sheridan’s reinforcements.
“This Brigade led the column in the formal entry, and at the City Hall
halted while I reported to Major-General Weitzel,” says General
Ripley. “General Weitzel had taken up his position on the platform of
the high steps at the east front of the Confederate Capitol, and
there, looking down into a gigantic crater of fire, suffocated and
blinded with the vast volumes of smoke and cinders which rolled up
over and enveloped us, he assigned me and my brigade to the
apparently hopeless task of stopping the conflagration, and
suppressing the mob of stragglers, released criminals, and negroes,
who had far advanced in pillaging the city. He had no suggestions to](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-63-320.jpg)
![make, no orders to give, except to strain every nerve to save the
city, crowded as it was with women and children, and the sick and
wounded of the Army of Northern Virginia.
“After requesting Major-General Weitzel to have all the other troops
marched out of the city, I took the Hon. Joseph Mayo, then Mayor of
Richmond, with me to the City Hall, where I established my
headquarters. With the help of the city officials, I distributed my
regiment quickly in different sections. The danger to the troops
engaged in this terrific fire-fighting was infinitely enhanced by the
vast quantities of powder and shells stored in the section burning.
Into this sea of fire, with no less courage and self-devotion than as
though fighting for their own firesides and families, stripped and
plunged the brave men of the First Brigade.
“Meanwhile, detachments scoured the city, warning every one from
the streets to their houses.... Every one carrying plunder was
arrested.... The ladies of Richmond thronged my headquarters,
imploring protection. They were sent to their homes under the
escort of guards, who were afterwards posted in the center house of
each block, and made responsible for the safety of the
neighborhood.... Many painful cases of destitution were brought to
light by the presence of these safeguards in private houses, and the
soldiers divided rations with their temporary wards, in many cases,
until a general system of relief was organised.”[2]
THE COMING OF LINCOLN](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-64-320.jpg)
![Major Sutherlin had been a strong Union man. Mrs. Sutherlin has
told me how her husband voted against secession in the first
convention to which he was a delegate, and for it in the second,
with deep regret. “I saw in that convention,” he told his wife,
“strong, reserved men, men of years and dignity, sign the Secession
Ordinance while tears coursed down their cheeks.”
It is just to rehearse such things of men who were called “traitors”
and “rebels.” It is just to remember how Jefferson Davis tried to
prevent secession. His letters to New England societies, his speeches
in New England and in Congress, testified to his deep and fervent
desire for the “preservation of the bond between the States,” the
“love of the Union in our hearts,” and “the landmarks of our fathers.”
But he believed in States’ Rights as fervently as in Union of States;
he believed absorption of State sovereignty into central sovereignty
a violation of the Constitution. Long before secession (1847) he
declined appointment of Brigadier General of Mississippi Volunteers
from President Polk on the ground that the central government was
not vested by the Constitution with power to commission officers of
State Militia, the State having this authority.[3]
Americans should not forget that this man entered the service of the
Union when a lad; that his father and uncles fought in the
Revolution, his brothers in the War of 1812. West Point holds
trophies of his skill as a commander and of his superb gallantry on
the fields of Mexico. That splendid charge without bayonets through
the streets of Monterey almost to the Plaza, and the charge at
Buena Vista, are themes to make American blood tingle! Their leader
was not a man to believe in defeat as long as a ray of hope was left.](https://image.slidesharecdn.com/1069672-250602090849-6ad2c907/85/Information-Modelling-And-Knowledge-Bases-Xix-H-Jaakkola-Y-Kiyoki-81-320.jpg)
Information Modelling And Knowledge Bases Xix H Jaakkola Y Kiyoki
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- 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, R. Dieng-Kuntz, N. Guarino, J.N. Kok, J. Liu, R. López de Mántaras, R. Mizoguchi, M. Musen, S.K. Pal and N. Zhong Volume 166 Recently published in this series Vol. 165. A.R. Lodder and L. Mommers (Eds.), Legal Knowledge and Information Systems – JURIX 2007: The Twentieth Annual Conference Vol. 164. J.C. Augusto and D. Shapiro (Eds.), Advances in Ambient Intelligence Vol. 163. C. Angulo and L. Godo (Eds.), Artificial Intelligence Research and Development Vol. 162. T. Hirashima et al. (Eds.), Supporting Learning Flow Through Integrative Technologies Vol. 161. H. Fujita and D. Pisanelli (Eds.), New Trends in Software Methodologies, Tools and Techniques – Proceedings of the sixth SoMeT_07 Vol. 160. I. Maglogiannis et al. (Eds.), Emerging Artificial Intelligence Applications in Computer Engineering – Real World AI Systems with Applications in eHealth, HCI, Information Retrieval and Pervasive Technologies Vol. 159. E. Tyugu, Algorithms and Architectures of Artificial Intelligence Vol. 158. R. Luckin et al. (Eds.), Artificial Intelligence in Education – Building Technology Rich Learning Contexts That Work Vol. 157. B. Goertzel and P. Wang (Eds.), Advances in Artificial General Intelligence: Concepts, Architectures and Algorithms – Proceedings of the AGI Workshop 2006 Vol. 156. R.M. Colomb, Ontology and the Semantic Web Vol. 155. O. Vasilecas et al. (Eds.), Databases and Information Systems IV – Selected Papers from the Seventh International Baltic Conference DB&IS’2006 Vol. 154. M. Duží et al. (Eds.), Information Modelling and Knowledge Bases XVIII Vol. 153. Y. Vogiazou, Design for Emergence – Collaborative Social Play with Online and Location-Based Media ISSN 0922-6389
- 7. Information Modelling and Knowledge Bases XIX Edited by Hannu Jaakkola Tampere University of Technology, Finland Yasushi Kiyoki Keio University, Japan and Takahiro Tokuda Tokyo Institute of Technology, Japan Amsterdam • Berlin • Oxford • Tokyo • Washington, DC
- 8. © 2008 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 978-1-58603-812-0 Library of Congress Control Number: 2007940891 Publisher IOS Press Nieuwe Hemweg 6B 1013 BG Amsterdam Netherlands fax: +31 20 687 0019 e-mail: order@iospress.nl Distributor in the UK and Ireland Distributor in the USA and Canada Gazelle Books Services Ltd. IOS Press, Inc. White Cross Mills 4502 Rachael Manor Drive Hightown Fairfax, VA 22032 Lancaster LA1 4XS USA United Kingdom fax: +1 703 323 3668 fax: +44 1524 63232 e-mail: iosbooks@iospress.com e-mail: sales@gazellebooks.co.uk LEGAL NOTICE The publisher is not responsible for the use which might be made of the following information. PRINTED IN THE NETHERLANDS
- 9. Information Modelling and Knowledge Bases XIX v H. Jaakkola et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. Preface In the last decades information modelling and knowledge bases have become hot topics not only in academic communities related to information systems and computer science but also in business areas where information technology is applied. The 17th European-Japanese Conference on Information Modelling and Knowl- edge Bases, EJC 2007, continues the series of events that originally started as a co- operation between Japan and Finland as far back as the late 1980’s. Later (1991) the geographical scope of these conferences expanded to cover all of Europe as well as countries outside Europe other than Japan. The EJC conferences constitute a world-wide 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 researches as well as practitioners dealing with in- formation modelling and knowledge bases. Thus the main topics of the EJC confer- ences target the variety of themes in the domain of information modelling, conceptual analysis, design and specification of information systems, ontologies, software engi- neering, knowledge and process management, data and knowledge bases. We also aim at applying new progressive theories. To this end much attention is being paid also to theoretical disciplines including cognitive science, artificial intelligence, logic, linguis- tics and analytical philosophy. In order to achieve the EJC targets, an international programme committee se- lected 19 full papers, 8 short papers, 4 position papers and 3 poster papers in the course of a rigorous reviewing process including 34 submissions. The selected papers cover many areas of information modelling, namely theory of concepts, database semantics, knowledge representation, software engineering, WWW information management, context-based information retrieval, ontological technology, image databases, temporal and spatial databases, document data management, process management, and many others. The conference would not have been a success without the effort of many people and organizations. In the Programme Committee, 37 reputable researchers devoted a good deal of effort to the review process in order to select the best papers and create the EJC 2007 programme. We are very grateful to them. Professors Yasushi Kiyoki and Takehiro Tokuda were acting as co-chairs of the programme committee. The Tampere University of Technology in Pori, Finland, promoted the conference in its capacity as organizer: Professor Hannu Jaakkola acted as conference leader and Ms. Ulla Nevan- ranta as conference secretary. They took care of both the various practical aspects nec- essary for the smooth running of the conference and for arranging the conference pro- ceedings in the form of a book. The conference is sponsored by the City of Pori, Sata- kunnan Osuuskauppa, Satakunnan Puhelin, Secgo Software, Nokia, Ulla Tuominen Foundation and Japan Scandinavia Sasakawa Foundation. We gratefully appreciate the efforts of everyone who lent a helping hand.
- 10. vi We are convinced that the conference will prove to be productive and fruitful to- ward advancing the research and application of information modelling and knowledge bases. The Editors Hannu Jaakkola Yasushi Kiyoki Takahiro Tokuda
- 11. vii Programme Committee Co-Chairs Hannu Jaakkola, Tampere University of Technology, Pori, Finland Hannu Kangassalo, University of Tampere, Finland Yasushi Kiyoki, Keio University, Japan Takahiro Tokuda, Tokyo Institute of Technology, Japan Members Akaishi Mina, University of Tokyo, Japan Bielikova Maria, Slovak University of Technology, Slovakia Brumen Boštjan, University of Maribor, Slovenia Carlsson Christer, Åbo Akademi, Finland Charrel Pierre-Jean, Université Toulouse2, France Chen Xing, Kanagawa Institute of Technology, Japan Ďuráková Daniela, VSB – Technical University Ostrava, Czech Republic Duží Marie, VSB – Technical University of Ostrava, Czech Republic Funyu Yutaka, Iwate Prefectural University, Japan Haav Hele-Mai, Institute of Cybernetics, Estonia Heimbürger Anneli, University of Jyväskylä, Finland Henno Jaak,Tallinn Technical University, Estonia Hosokawa Yoshihide, Nagoya Institute of Technology, Japan Iivari Juhani, University of Oulu, Finland Jaakkola Hannu, Tampere University of Technology, Pori, Finland Kalja Ahto, Tallinn Technical University, Estonia Kawaguchi Eiji, Kyushu Institute of Technology, Japan Leppänen Mauri, University of Jyväskylä, Finland Link Sebastian, Massey University, New Zealand Mikkonen Tommi, Tampere University of Technology, Finland Mirbel Isabelle, Université de Nice Sophia Antipolis, France Multisilta Jari, Tampere University of Technology, Pori, Finland Nilsson Jørgen Fischer, Denmark Technical University, Denmark Oinas-Kukkonen Harri, University of Oulu, Finland Palomäki Jari, Tampere University of Technology, Pori, Finland Pokorny Jaroslav, Charles University Prague, Czech Republic Richardsson Ita, University of Limerick, Ireland Roland Hausser, Erlangen University, Germany Sasaki Hideyasu, Ritsumeikan University, Japan Suzuki Tetsuya, Shibaura Institute of Technology, Japan Thalheim Bernhard, Kiel University, Germany Tyrväinen Pasi, University of Jyväskylä, Finland Vojtas Peter, Charles University Prague, Czech Republic Wangler Benkt, Skoevde University, Sweden
- 12. viii Watanabe Yoshimichi, Yamanashi University, Japan Yoshida Naofumi, Komazawa University, Japan Yu Jeffery Xu, Chinese University of Hong Kong, Hong Kong Organizing Committee Professor Hannu Jaakkola, Tampere University of Technology, Pori, Finland Dept. secretary Ulla Nevanranta, Tampere University of Technology, Pori, Finland Professor Eiji Kawaguchi, Kyushu Institute of Technology, Japan Steering Committee Professor Eiji Kawaguchi, Kyushu Institute of Technology, Japan Professor Hannu Kangassalo, University of Tampere, Finland Professor Hannu Jaakkola, Tampere University of Technology, Pori, Finland Professor Setsuo Ohsuga, Japan Professor Marie Duží, VSB – Technical University of Ostrava, Czech Republic
- 13. ix Contents Preface v Hannu Jaakkola, Yasushi Kiyoki and Takahiro Tokuda Programme Committee vii Comparing the Use of Feature Structures in Nativism and in Database Semantics 1 Roland Hausser Multi-Criterion Search from the Semantic Point of View (Comparing TIL and Description Logic) 21 Marie Duží and Peter Vojtáš A Semantic Space Creation Method with an Adaptive Axis Adjustment Mechanism for Media Data Retrieval 40 Xing Chen, Yasushi Kiyoki, Kosuke Takano and Keisuke Masuda Storyboarding Concepts for Edutainment WIS 59 Klaus-Dieter Schewe and Bernhard Thalheim A Model of Database Components and Their Interconnection Based upon Communicating Views 79 Stephen J. Hegner Creating Multi-Level Reflective Reasoning Models Based on Observation of Social Problem-Solving in Infants 100 Heikki Ruuska, Naofumi Otani, Shinya Kiriyama and Yoichi Takebayashi CMO – An Ontological Framework for Academic Programs and Examination Regulations 114 Richard Hackelbusch Reusing and Composing Habitual Behavior in Video Browsing 134 Akio Takashima and Yuzuru Tanaka Concept Modeling in Multidisciplinary Research Environment 142 Jukka Aaltonen, Ilkka Tuikkala and Mika Saloheimo Extensional and Intensional Aspects of Conceptual Design 160 Elvira Locuratolo and Jari Palomaki Emergence of Language: Hidden States and Local Environments 170 Jaak Henno Frameworks for Intellectual Property Protection on Multimedia Database Systems 181 Hideyasu Sasaki and Yasushi Kiyoki
- 14. x Wavelet and Eigen-Space Feature Extraction for Classification of Metallography Images 190 Pavel Praks, Marcin Grzegorzek, Rudolf Moravec, Ladislav Válek and Ebroul Izquierdo Semantic Knowledge Modeling in Medical Laboratory Environment for Drug Usage: CASE Study 200 Anne Tanttari, Kimmo Salmenjoki and Lorna Uden Towards Automatic Construction of News Directory Systems 208 Bin Liu, Pham Van Hai, Tomoya Noro and Takehiro Tokuda A System Architecture for the 7C Knowledge Environment 217 Teppo Räisänen and Harri Oinas-Kukkonen Inquiry Based Learning Environment for Children 237 Marjatta Kangassalo and Eva Tuominen A Perspective Ontology and IS Perspectives 257 Mauri Leppänen The Improvement of Data Quality – A Conceptual Model 276 Tatjana Welzer, Izidor Golob, Boštjan Brumen, Marjan Družovec, Ivan Rozman and Hannu Jaakkola Knowledge Cluster Systems for Knowledge Sharing, Analysis and Delivery Among Remote Sites 282 Koji Zettsu, Takafumi Nakanishi, Michiaki Iwazume, Yutaka Kidawara and Yasushi Kiyoki A Formal Ontology for Business Process Model TAP: Tasks-Agents-Products 290 Souhei Ito, Shigeki Hagihara and Naoki Yonezaki A Proposal for Student Modelling Based on Ontologies 298 Angélica de Antonio, Jaime Ramírez and Julia Clemente Ontology-Based Support of Knowledge Evaluation in Higher Education 306 Andrea Kő, András Gábor, Réka Vas and Ildikó Szabó When Cultures Meet: Modelling Cross-Cultural Knowledge Spaces 314 Anneli Heimbürger Process Dimension of Concepts 322 Vaclav Repa E-Government: On the Way Towards Frameworks for Application Engineering 330 Marie-Noëlle Terrasse, Marinette Savonnet, Eric Leclercq, George Becker, Thierry Grison, Laurence Favier and Carlo Daffara A Personal Web Information/Knowledge Retrieval System 338 Hao Han and Takehiro Tokuda A Personal Information Protection Model for Web Applications by Utilizing Mobile Phones 346 Michiru Tanaka, Jun Sasaki, Yutaka Funyu and Yoshimi Teshigawara
- 15. xi Manufacturing Roadmaps as Information Modelling Tools in the Knowledge Economy 354 Augusta Maria Paci Metadata Extraction and Retrieval Methods for Taste-Impressions with Bio-Sensing Technology 359 Hanako Kariya and Yasushi Kiyoki An Ontological Framework for Modeling Complex Cooperation Contexts in Organizations 379 Bendoukha Lahouaria Information Modelling and Knowledge Bases for Interoperability Solution in Security Area 384 Ladislav Buřita and Vojtĕch Ondryhal On the Construction of Ontologies Based on Natural Language Semantic 389 Terje Aaberge Author Index 395
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- 17. Comparing the Use of Feature Structures in Nativism and in Database Semantics Roland Hausser Universität Erlangen-Nürnberg Abteilung Computerlinguistik (CLUE) rrh@linguistik.uni-erlangen.de Abstract Linguistics has always been a field with a great diversity of schools and sub-schools. This has naturally led to the question of whether different grammatical analyses of the same sentence are in fact equivalent or not. With the formalization of grammars as generative rule systems, beginning with the “Chomsky revolution” in the late nineteen fifties, it became possible to answer such questions in those fortunate instances in which the competing analyses were sufficiently formalized. An early example is the comparison of Context-Free Phrase Structure Grammar (CF- PSG) and Bidirectional Categorial Grammar (BCG), which were shown to be weakly equivalent by Gaifman 1961. More recently, the question arose with respect to the lan- guage classes and the complexity hierarchies of Phrase Structure Grammar (PS-grammar) and of Left-Associative Grammar (LA-grammar), which were shown to be orthogonal to each other (TCS’92). Here we apply the question to the use of feature structures in contemporary schools of Nativism on the one hand, and in Database Semantics (DBS) on the other. The practical purpose is to determine whether or not the grammatical analyses of Nativism based on constituent structure can be used in Database Semantics. 1 Introduction: Constituent Structure in Nativism In contemporary linguistics, most schools are based on constituent structure analysis. Exam- ples are GB (Chomsky 1981), LFG (Bresnan ed. 1982), GPSG (Gazdar et al. 1985), and HPSG (Pollard and Sag 1987, 1994). Related schools are DCG (Pereira and Warren 1980), FUG (Kay 1992), TAG (Vijay-Shanker and Joshi 1988), and CG (Kay 2002). For historical reasons and because of their similar goals and methods, these schools may be jointly referred to as variants of Nativism.1 Constituent structure is defined in terms of phrase structure trees which fulfill the following conditions: 1.1 DEFINITION OF CONSTITUENT STRUCTURE 1. Words or constituents which belong together semantically must be dominated directly and exhaustively by a node. 2. The lines of a constituent structure may not cross (non-tangling condition). 1 Nativism is so-called because it aims at characterizing the speaker-hearer’s innate knowledge of language (competence) – excluding the use of language in communication (performance). Information Modelling and Knowledge Bases XIX H. Jaakkola et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. 1
- 18. According to this definition, the first of the following two phrase structure trees is a linguis- tically correct analysis, while the second is not: 1.2 CORRECT AND INCORRECT CONSTITUENT STRUCTURE ANALYSIS John John Julia SP Julia incorrect correct V knows V knows NP VP NP NP NP S S There is common agreement among Nativists that the words knows and John belong more closely together semantically than the words Julia and knows.2 Therefore, only the tree on the left is accepted as a correct grammatical analysis. Formally, however, both phrase structure trees are equally well-formed. Moreover, the number of possible trees grows exponentially with the length of the sentence.3 The problem is that such a multitude of phrase structure trees for the same sentence would be meaningless linguistically, if they were all equally correct. It is for this reason that constituent structure as defined in 1.1 is crucial for phrase structure grammar (PS-grammar): constituent structure is the only known principle4 for excluding most of the possible trees. Yet it has been known at least since 1960 (cf. Bar-Hillel 1964, p. 102) that there are certain constructions of natural language, called “discontinuous elements,” which do not fulfill the definition of constituent structure. Consider the following examples: 1.3 CONSTITUENT STRUCTURE PARADOX: VIOLATING CONDITION 1 DET N DE NP NP V VP S looked the word up Suzy Here the lines do not cross, satisfying the second condition of Definition 1.1. The analysis violates the first condition, however, because the semantically related expressions looked – up, or rather the nodes V (verb) and DE (discontinuous element) dominating them, are not exhaustively dominated by a node. Instead, the node directly dominating V and DE also dominates the NP the word. 2 To someone not steeped in Nativist linguistics, these intuitions may be difficult to follow. They are related to the substitution tests of Z. Harris, who was Chomsky’s teacher. 3 If loops like A → ... A are permitted in the rewrite rules, the number of different trees over a finite sentence is infinite! 4 Historically, the definition of constituent structure is fairly recent, based on the movement and substitution tests of American Structuralism in the nineteen thirties and forties. R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 2
- 19. 1.4 CONSTITUENT STRUCTURE PARADOX: VIOLATING CONDITION 2 DET N DE NP NP V S looked the word up VP VP Suzy Here the semantically related subexpressions looked and up are dominated directly and ex- haustively by a node, thus satisfying the first condition of Definition 1.1. The analysis violates the second condition, however, because the lines in the tree cross. Rather than giving up constituent structure as the intuitive basis of their analysis, the differ- ent schools of Nativism extended the formalism of context-free phrase structure with addi- tional structures and mechanisms like transformations (Chomsky 1965), f-structures (Bresnan ed. 1982), meta-rules (Gazdar et al. 1985), constraints (Pollard and Sag 1987, 1994), the ad- joining of trees (Vijay-Shanker and Joshi 1988), etc. In recent years, these efforts to extend the descriptive power of context-free phrase structure grammar have converged in the wide- spread use of recursive feature structures with unification. Consider the following example, which emphasizes what is common conceptually to the different variants of Nativism. 1.5 RECURSIVE FEATURE STRUCTURES AND UNIFICATION S NP VP NP V derivation structure phrase lexical lookup unification tense: pres subj: obj: Julia knows John tense: pres subj: obj: tense: pres obj: subj: noun: Julia gen: fem verb: know noun: John gen: masc verb: know noun: John gen: masc verb: know noun: Julia gen: fem noun: John gen: masc num: sg num: sg num: sg num: sg num: sg result R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 3
- 20. As in 1.2 (correct tree), the analysis begins with the start symbol S, from which the phrase structure tree is derived by substituting NP and VP for S, etc., until the terminal nodes Ju- lia, knows, and John are reached (phrase structure derivation). Next the terminal nodes are replaced by feature structures via lexical lookup. Finally, the lexical feature structures are unified (indicated by the dotted arrows), resulting in one big recursive feature structure (result). The order of unification mirrors the derivation of the phrase structure tree. On the one hand, the use of feature structures provides for many techniques which go be- yond the context free phrase structure tree, such as a differentiated lexical analysis, structure sharing (a.k.a. token identity), a truth-conditional semantic interpretation based on lambda calculus, etc. On the other hand, this method greatly increases the mathematical complexity from polynomial to exponential or undecidable. Also, the constituent structure paradox, as a violation of Definition 1.1, remains. 2 Elimination of Constituent Structure in LA-grammar Instead of maintaining constituent structure analysis when it is possible (e.g. 1.2, correct tree) and taking exception to it when it is not (e.g. 1.3), Left-Associative Grammar com- pletely abandoned constituent structure as defined in 1.1 by adopting another, more basic principle. This principle is the time-linear structure of natural language – in accordance with de Saussure’s 1913/1972 second law (principe seconde). Time-linear means linear like time and in the direction of time. Consider the following reanalysis of Example 1.2 within Left-Associative Grammar (LA- grammar) as presented in NEWCAT’86: 2.1 TIME-LINEAR ANALYSIS OF Julia knows John IN LA-GRAMMAR Julia knows (nm) (a’ v) Julia knows John (nm) (v) Julia knows John (s3’ a’ v) Given an input sentence or a sequence of input sentences (text), LA-grammar always com- bines a “sentence start,” e.g. Julia, and a “next word,” e.g. knows, into a new sentence start, e.g. Julia knows. This time-linear procedure starts with the first word and continues until there is no more next word available in the input. In LA-grammar, the intuitions about what “belongs semantically together” (which under- lie the definition of constituent structure 1.1) are reinterpreted in terms of functor-argument structure and coded in categories which are defined as lists of one or more category segments. For example, in 2.1 the category segment nm (for name) of Julia cancels the first valency po- sition s3’ (for nominative singular third person) of the category (s3’ a’ v) of knows, whereby Julia serves as the argument and knows as the functor. Then the resulting sentence start Ju- lia knows of the category (a’ v) serves as the functor and John as the argument. The result is a complete sentence, represented as a verb without unfilled valency positions, i.e., as the category (v). Next consider the time-linear reanalysis of the example with a discontinuous element (cf. 1.3 and 1.4): R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 4
- 21. 2.2 TIME-LINEAR ANALYSIS OF Suzy looked the word up (nm) looked (n’ a’ up’ v) (a’ up’ v) the (nn’ np) (nn’ up’ v) word (nn) (up’ v) up (v) (up) Suzy Suzy looked Suzy looked the Suzy looked the word Suzy looked the word up Here the discontinuous element up is treated like a valency filler for the valency position up’ in the lexical category (n’ a’ up’ v) of looked. Note the strictly time-linear addition of the “constituent” the word: the article the has the category (nn’ np) such that the category segment np cancels the valency position a’ in the category (a’ up’ v) of Suzy looked, while the category segment nn’ is added in the result category (nn’ up’ v) of Suzy looked the. In this way, the obligatory addition of a noun after the addition of a determiner is ensured. The time-linear analysis of LA-grammar is based on formal rules which compute possible continuations. Consider the following example (explanations in italics): 2.3 EXAMPLE OF AN LA-GRAMMAR RULE APPLICATION (i) rule name (ii) ss (iii) nw (iv) ss’ (v) RP Nom+Fverb: (NP) (NP’ X V) ⇒ (X V) {Fverb+Main, ...} | | | | | | matching and binding (nm) (s3’ a’ v) (a’ v) Julia knows Julia knows An LA-grammar rule consists of (i) a rule name, here Nom+Fverb, (ii) a pattern for the sen- tence start ss, here (NP), (iii) a pattern for the next word nw, here (NP’ X V), (iv) a pattern for the resulting sentence start ss’, here (X V), and (v) a rule package RP, here {Fverb+Main, ...}. The patterns for (ii) ss, (iii) nw, and (iv) ss’ are coded by means of restricted variables, which are matched and vertically bound with corresponding category segments of the lan- guage input. For example, in 2.3 the variable NP at the rule level is bound to the category segment nm at the language level, the variable NP’ is bound to the category segment s3’, etc. If the matching of variables fails with respect to an input (because a variable restriction is violated), the rule application fails. If the matching of variables is successful, the categorial operation (represented by (ii) ss, (iii) nw, and (iv) ss’) is performed and a new sentence start is derived. That the categorial operation defined at the rule level can be executed at the language level is due to the vertical binding of the rule level variables to language level constants. After the successful application of an LA-grammar rule, the rules in its (v) rule package RP are applied to the resulting sentence start (iv) ss’ and a new next word. A crucial property of LA-grammar rules is that they have an external interface, defined in terms of the rule level variables and their vertical matching with language level category segments. This is in contradistinction to the rewrite rules of phrase structure grammar: they do not have any external interface because all phrase structure trees are derived from the same initial S node, based on the principle of possible substitutions. R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 5
- 22. 3 From LA-grammar to Database Semantics The external interfaces of LA-grammar rules, originally introduced for computing the pos- sible continuations of a time-linear derivation, open the transition from a sign-oriented ap- proach to an agent-oriented approach of natural language analysis.5 While a sign-oriented approach analyses sentences in isolation, an agent-oriented approach analyses sentences as a means to transfer information from the mind of the speaker to the mind of the hearer. In Database Semantics, LA-grammar is used for an agent-oriented approach to linguistics which aims at building an artificial cognitive agent (talking robot). This requires the design of (i) interfaces for recognition and action, (ii) a data structure suitable for storing and retrieving content, and (iii) an algorithm for (a) reading content in during recognition, (b) processing content during thought, and (c) reading content out during action. Moreover, the data structure must represent non-verbal cognition at the context level as well as verbal cognition at the language level. Finally, the two levels must interact in such a way as to model the speaker mode (mapping from the context level to the language level) and the hearer mode (mapping from the language level to the context level). Consider the representation of these requirements in the following schema: 3.1 STRUCTURING CENTRAL COGNITION IN AGENTS WITH LANGUAGE peripheral cognition central cognition sign recognition sign synthesis context action contex recognition language component context component pragmatics Cognitive Agent External Reality theory of grammar theory of language The interfaces of recognition and action are based on pattern matching. At the context level, the patterns are defined as concepts, which are also used for coding and storing content. At the language level, the concepts of the context level are reused as the literal meanings of content words. In this way, the lexical semantics is based on procedurally defined concepts rather than the metalanguage definitions of a truth-conditional semantics (cf. NLC’06, Chapter 2 and Section 6.2). The data structure for coding and storing content at the context level is based on flat (non- recursive) feature structures called proplets (in analogy to “droplets”). Proplets are so-called because they serve as the basic elements of concatenated propositions. Consider the follow- ing example showing the simplified proplets representing the content resulting from an agent perceiving a barking dog (recognition) and running away (action): 3.2 CONTEXT PROPLETS REPRESENTING dog barks. (I) run. ⎡ ⎢ ⎢ ⎢ ⎣ sur: noun: dog fnc: bark prn: 22 ⎤ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ sur: verb: bark arg: dog nc: 23 run prn: 22 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ sur: verb: run arg: moi pc: 22 bark prn: 23 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ 5 Clark 1996 distinguishes between the language-as-product and the language-as-action traditions. R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 6
- 23. The semantic relation between the first two proplets is intrapropositional functor-argument structure, and is coded as follows: The first proplet with the core feature [noun: dog] specifies the associated functor with the intrapropositional continuation feature [fnc: bark], while the second proplet with the core feature [verb: bark] specifies its associated argument with [arg: dog] (bidirectional pointering). That the first and the second proplet belong to the same proposition is indicated by their having the same prn (proposition number) value, namely 22. The semantic relation between the second and the third proplet is extrapropositional coor- dination. That these two proplets belong to different propositions is indicated by their having different prn values, namely 22 and 23, respectively. Their coordination relation is coded in the second proplet by the extrapropositional continuation feature [nc: 23 run] and in the third proplet by [pc: 22 bark], whereby the attributes nc and pc stand for “next conjunct” and “previous conjunct,” respectively. The values of the nc and pc attributes are the proposition number and the core value of the verb of the coordinated proposition. By coding the semantic relations between proplets solely in terms of attributes and their values, proplets can be stored and retrieved according to the needs of one’s database, without any of the graphical restrictions induced by phrase structure trees. Furthermore, by using sim- ilar proplet at the levels of language and context, the matching between the two levels during language interpretation (hearer mode) and language production (speaker mode) is structurally straightforward. Consider the following example in which the context level content of 3.2 is matched with corresponding language proplets containing German surfaces: 3.3 MATCHING BETWEEN THE LANGUAGE AND THE CONTEXT LEVEL sur: bellt arg: dog prn: 122 nc: 123 run sur: fliehe prn: 123 pc: 122 bark arg: moi sur: sur: fnc: bark arg: dog sur: prn: 22 prn: 23 nc: 23 run pc: 22 bark prn: 22 arg: moi (horizontal relations) (horizontal relations) matching internal (vertical relations) sur: Hund fnc: bark prn: 122 noun: verb: verb: noun: verb: dog bark run dog bark run verb: language level: context level: The proplets at the language and the context level are alike except that the sur (surface) attributes of context proplets have an empty value, while those of the language proplets have a language-dependent surface, e.g. Hund, as value. On both levels, the intra- and extrapropositional relations are coded by means of attribute values (horizontal relations, indicated by dotted lines). The reference relation between cor- responding proplets at the two levels, in contrast, is based on matching (vertical relations, indicated by double arrows). Simply speaking, the matching between a language and a con- text proplet is successful if they have the same attributes and their values are compatible. Even though the vertical matching takes place between individual proplets, the horizontal semantic relations holding between the proplets at each of the two levels are taken into ac- count as well. Assume, for example, that the noun proplet dog at the language level has the fnc value bark, while the corresponding proplet at the context level had the fnc value sleep. In this case, the two proplets would be vertically incompatible – due to their horizontal rela- tions to different verbs, coded as different values of their respective fnc attributes. Having described the data structure of Database Semantics, let us turn next to its algorithm. For natural language communication, the time-linear algorithm of LA-grammar is used in three different variants: (i) in the hearer mode, an LA-hear grammar interprets sentences of natural language as sets of proplets ready to be stored in the database of the cognitive agent, R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 7
- 24. (ii) in the think mode, an LA-think grammar navigates along the semantic relations between proplets, and (iii) in the speaker mode an LA-speak grammar verbalizes the proplets traversed in the think mode as surfaces of a natural language. Consider the following LA-hear derivation of Julia knows John in Database Semantics. 3.4 TIME-LINEAR HEARER-MODE ANALYSIS OF Julia knows John lexical lookup syntactic−semantic parsing: 1 2 John prn: arg: fnc: noun: Julia prn: 1 prn: verb: know arg: prn: fnc: noun: Julia result of syntactic−semantic parsing: verb: know noun: Julia fnc: know prn: 1 prn: 1 arg: Julia John noun: John prn: 1 verb: know noun: Julia fnc: know prn: 1 prn: 1 arg: Julia noun: John fnc: prn: fnc: prn: knows Julia noun: John fnc: know verb: know This derivation is similar to 2.1 in that it is strictly time-linear. The differences are mostly in the format. While 2.1 must be read bottom up, 3.4 starts with the lookup of lexical proplets and must be read top down. Furthermore, while the ss and nw in 2.1 each consist of a surface and a category defined as a list, the ss and nw in 3.4 consist of proplets. Finally, while the output of 2.1 is the whole derivation (like a tree in a sign-oriented approach), the output of 3.4 is a set of proplets (cf. result) ready to be stored in the database. The rules of an LA-hear grammar have patterns for matching proplets rather than categories (as in 2.3). This is illustrated by the following example (explanations in italics): 3.5 EXAMPLE OF AN LA-hear RULE APPLICATION (i) rule name (ii) ss-pattern (iii) nw-pattern (iv) operations (v) rule package rule level NOM+FV: noun: α fnc: verb: β arg: copy α nw.arg copy β ss.fnc {FV+OBJ, ...} matching and binding proplet level ⎡ ⎢ ⎣ noun: Julia fnc: prn: 1 ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ verb: know arg: prn: ⎤ ⎥ ⎦ This rule resembles the one illustrated in 2.3 in that it consists of (i) a rule name, (ii) a pattern for the ss, (iii) a pattern of the nw, and (v) a rule package. It differs from 2.3, however, in that the resulting sentence start (iv) ss’ is replaced by a set of operations. During matching, the variables, here α and β, of the rule level are vertically bound to cor- responding values at the proplet level. This is the basis for executing the rule level operations at the proplet level. In 3.5, the operations code the functor-argument relation between the subject and the verb by copying the core value of the noun into the arg slot of the verb and the core value of the verb into the fnc slot of the noun. In the schematic derivation 3.4, the copying is indicated by the arrows. The result of the rule application 3.5 is as follows: R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 8
- 25. 3.6 RESULT OF THE LA-hear RULE APPLICATION SHOWN IN 3.5 ⎡ ⎢ ⎣ noun: Julia fnc: know prn: 1 ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ verb: know arg: Julia prn: 1 ⎤ ⎥ ⎦ In the next time-linear combination, the current result serves as the sentence start, while lexical lookup provides the proplet John as the next word (cf. 3.4, line 2). The example with a discontinuous element (cf. 2.2 and 2.3) is reanalyzed in the hearer mode of Database Semantics as follows: 3.7 HEARER MODE ANALYSIS OF Suzy looked the word up fnc: prn: noun: word fnc: prn: noun: word lexical lookup syntactic−semantic parsing: 1 2 looked the word up fnc: prn: noun: n_1 prn: 2 fnc: prn: noun: n_1 prn: 2 3 prn: 2 noun: n_1 prn: 2 prn: 2 prn: 2 prn: 2 prn: 2 4 noun: word 5 result of syntactic−semantic parsing: prn: 2 prn: 2 prn: 2 noun: word verb: look up prn: adj: up mdd: prn: adj: up mdd: noun: Suzy arg: Suzy word prn: 2 prn: 2 prn: 2 noun: word noun: Suzy arg: Suzy word noun: Suzy arg: Suzy word noun: Suzy arg: Suzy n_1 noun: Suzy arg: Suzy prn: arg: fnc: prn: 2 prn: arg: prn: fnc: noun: Suzy Suzy noun: Suzy verb: look a_1 verb: look a_1 fnc: look a_1 fnc: look a_1 fnc: look a_1 fnc: look a_1 fnc: look a_1 verb: look a_1 verb: look a_1 verb: look a_1 verb: look a_1 fnc: look a_1 fnc: look a_1 fnc: look up fnc: look up One difference to the earlier LA-grammar analysis 2.2 is the handling of the determiner the. In its lexical analysis, the core value is the substitution value n_1. In line 2, this value is copied into the arg slot of look and the core value of look is copied into the fnc slot of the. In line 3, the core value of word is used to substitute all occurrences of the substitution value n_1, after which the nw proplet is discarded. This method is called function word absorption. An inverse kind of function word absorption is the treatment of the discontinuous element up. It is lexically analyzed as a standard preposition with the core attribute adj (cf. NLC’06, Chapter 15). In line 5, this preposition is absorbed into the verb, based on a suitable substitu- tion value. Thus, a sentence consisting of five words is represented by only three proplets. 4 The Cycle of Natural Language Communication In Database Semantics, the proplets resulting from an LA-hear derivation are stored in al- phabetically ordered token lines, called a word bank. Each token line begins with a concept, R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 9
- 26. corresponding to the owner record of a classic network database, followed by all proplets containing this concept as their core value in the order of their occurrence, serving as the member records of a network database (cf. Elmasri and Navathe 1989). Consider the following example. 4.1 TRANSFER OF CONTENT FROM THE SPEAKER TO THE HEARER prn: 1 prn: 1 prn: 1 prn: 1 prn: 1 prn: 1 verb: know arg: Julia John verb: know arg: Julia John know John noun: fnc: know noun: fnc: know Julia John Julia noun: fnc: know noun: fnc: know John Julia hearer: key−word−based storage speaker: retrieval−based navigation sign Julia knows John The word bank of the agent in the hearer mode (left) shows the token lines resulting from the LA-hear derivation 3.4. Due to the alphabetical ordering of the token lines, the sequencing of the proplets resulting from the LA-hear derivation is lost. Nevertheless, the semantic relations between them are maintained, due to their common prn value and the coding of the functor-argument structure in terms of attributes and values. The word bank of the agent in the speaker mode (right) contains the same proplets as the word bank on the left. Here a linear order is reintroduced by means of a navigation along the semantic relations defined between the proplets. This navigation from one proplet to the next serves as a model of thought and as the conceptualization of the speaker, i.e., as the specification of what to say and how to say it. The navigation from one proplet to the next is powered by an LA-think grammar. Consider the following rule application: 4.2 EXAMPLE OF AN LA-think RULE APPLICATION (i) rule name (ii) ss pattern (iii) nw pattern (iv) operations rule level V_N_V: ⎡ ⎢ ⎣ verb: β arg: X α Y prn: k ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ noun: α fnc: β prn: k ⎤ ⎥ ⎦ output position ss mark α ss matching and binding proplet level ⎡ ⎢ ⎣ verb: know arg: Julia John prn: 1 ⎤ ⎥ ⎦ (v) rule package {V_N_V, ...} R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 10
- 27. By binding the variables β, α, and k to know, Julia, and 1, respectively, the next word pattern is specified at the rule level such that the retrieval mechanism of the database can retrieve (navigate to, traverse, activate, touch) the correct continuation at the proplet level: 4.3 RESULT OF THE LA-think RULE APPLICATION ⎡ ⎢ ⎣ verb: know arg: !Julia John prn: 1 ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ noun: Julia fnc: know prn: 1 ⎤ ⎥ ⎦ In order to prevent repeated traversal of the same proplet,6 the arg value currently retrieved is marked with “!” (cf. NLC’06, p. 44). The autonomous navigation through the content of a word bank, powered by the rules of an LA-think grammar, is used not only for conceptualization in the speaker mode, but also for inferencing and reasoning in general. Providing a data structure suitable to (i) support navi- gation was one of the four main motivations for changing from the NEWCAT’86 notation of LA-grammar illustrated in 2.1, 2.2, and 2.3 to the NLC’06 notation illustrated in 3.4, 3.5, and 3.7. The other three motivations are (ii) the matching between the levels of language and con- text (cf. 3.3), (iii) a more detailed specification of lexical items, and (iv) a descriptively more powerful and more transparent presentation of the semantic relations, i.e., functor-argument structure, coordination, and coreference. A conceptualization defined as a time-linear navigation through content makes language production relatively straightforward: If the speaker decides to communicate a navigation to the hearer, the core values of the proplets traversed by the navigation are translated into their language-dependent counterparts and realized as external signs. In addition to this language- dependent lexicalization of the universal navigation, the language production system must provide language-dependent 1. word order, 2. function word precipitation (as the inverse of function word absorption), 3. word form selection for proper agreement. These tasks are handled by language-dependent LA-speak grammars in combination with language-dependent word form production. As an example of handling word order consider the production of the sentence Julia knows John from the set of proplets derived in 3.4: 4.4 PROPLETS UNDERLYING LANGUAGE PRODUCTION ⎡ ⎢ ⎣ verb: know arg: Julia John prn: 1 ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ noun: Julia fnc: know prn: 1 ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ noun: John fnc: know prn: 1 ⎤ ⎥ ⎦ Assuming that the navigation traverses the set by going from the verb to the subject noun to the object noun, the resulting sequence may be represented abstractly as VNN. Starting the navigation with the verb rather than the subject is because the connection be- tween propositions is coded by the nc and pc features of the verb (cf. 3.2 and NLC’06, Appendix A2). Assuming that n stands for a name, fv for a finite verb, and p for punctuation, the time-linear derivation of an abstract n fv n p surface from a VNN proplet sequence is based on the following incremental realization: 6 Relapse, see tracking principles, FoCL’99, p. 454. R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 11
- 28. 4.5 SCHEMATIC PRODUCTION OF Julia knows John. activated sequence realization i V i.1 n n V N i.2 fv n n fv V N i.3 fv n n n fv n V N N i.4 fv p n n n fv n p V N N In line i.1, the derivation begins with a navigation from V to N, based on LA-think. Also, the N proplet is realized as the n Julia by LA-speak. In line i.2, the V proplet is realized as the fv knows by LA-speak. In line i.3, LA-think continues the navigation to the second N proplet, which is realized as the n John by LA-speak. In line i.4, finally, LA-speak realizes the p . from the V proplet. This method can be used to realize not only a subject–verb–object surface (SVO) as in the above example, but also an SOV and (trivially) a VSO surface. It is based on the following principles: 4.6 PRINCIPLES FOR REALIZING SURFACES FROM A PROPLET SEQUENCE • Earlier surfaces may be produced from later proplets. Example: The initial n surface is achieved by realizing the second proplet in the acti- vated VN sequence first (cf. line i.1 in 4.5 above). • Later surfaces may be produced from earlier proplets. Example: The final punctuation p (full stop) is realized from the first proplet in the VNN sequence (cf. line i.4 in 4.5 above). Next consider the derivation of Suzy looked the word up., represented as an abstract n fv d nn de p surface, whereby n stands for a name, fv for a finite verb, d for a determiner, nn for a noun, de for a discontinuous element, and p for punctuation. 4.7 SCHEMATIC PRODUCTION OF Suzy looked the word up. activated sequence realization i V i.1 n n V N i.2 fv n n fv V N i.3 fv n d n fv d V N N i.4 fv n d nn n fv d nn V N N i.5 fv de n d nn n fv d nn de V N N i.6 fv de p n d nn n fv d nn de p V N N R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 12
- 29. This derivation of an abstract n fv d nn de p surface from an underlying VNN navigation shows two7 instances of function word precipitation: (i) of the determiner the from the second N proplet, and (ii) of the discontinuous element up from the initial V proplet. 5 “Constituent Structure” in Database Semantics? The correlation of the activated VNN sequence and the associated surfaces shown in line i.6 (left) of 4.7 may be spelled out more specifically as follows: 5.1 SURFACES REALIZED FROM PROPLETS IN A TRAVERSED SEQUENCE prn: 1 prn: 1 prn: 1 verb: noun: noun: look up word . look up the word fv de p n d nn Suzy Suzy arg: Suzy word fnc: look up fnc: look up This structure is like a constituent structure insofar as what belongs together semantically (cf. 1.1, condition 1) is realized from a single proplet. Like a deep structure in Chomsky 1965, however, the sequence fv de p n d nn of 5.1 does not constitute a well-formed surface. What is needed here is a transition to the well-formed surface sequence n fv d nn de p: 5.2 SURFACE ORDER RESULTING FROM AN INCREMENTAL REALIZATION prn: 1 prn: 1 prn: 1 verb: noun: noun: look up word the word up look . fv n d nn p de Suzy arg: Suzy word Suzy fnc: look up fnc: look up Instead of using a direct mapping like a transformation, Database Semantics establishes the correlation between the “deep” fv de p n d nn sequence 5.1 and the “surface” n fv d nn de p sequence 5.2 by means of a time-linear LA-think navigation with an associated incremental LA-speak surface realization, as shown schematically in 4.7 (for the explicit definition of the complete DBS1 and DBS2 systems of Database Semantics see NLC’06, Chapters 11–14). Note, however, that this “rediscovery” of constituent structure in the speaker mode of Data- base Semantics applies to the intuitions supported by the substitution and movement tests by Bloomfield 1933 and Harris 1951 (cf. FoCL’99, p. 155 f.), but not to the formal Definition 1.1 based on phrase structure trees. Nevertheless, given the extensive linguistic literature within phrase-structure-based Nativism, let us consider the possibility of translating formal constituent structures into proplets of Database Semantics. 6 On Mapping Phrase Structure Trees into Proplets Any context-free phrase structure tree may be translated into a recursive feature structure. A straightforward procedure is to define each node in the tree as a feature structure with the attributes node, up, and down. The value of the attribute node is the name of a node in 7 Actually, there is a third instance, namely the precipitation of the punctuation p from the V proplet. R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 13
- 30. the tree, for example node: S. The value of the attribute up specifies the next higher node, while the value of the attribute down specifies the next lower nodes. The linear precedence in the tree is coded over the order of the down values. Furthermore, the root node S is formally characterized by having an empty up value, while the terminal nodes are formally characterized by having empty down values. Consider the following example of systematically recoding the phrase structure tree 1.2 (correct) as a recursive feature structure: 6.1 RECODING A TREE AS A RECURSIVE FEATURE STRUCTURE ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ node: S up: down: ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ node: NP up: S down: ⎡ ⎢ ⎣ node: Julia up: NP down: ⎤ ⎥ ⎦ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ node: VP up: S down: ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ node: V up: VP down: ⎡ ⎢ ⎣ node: knows up: V down: ⎤ ⎥ ⎦ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ node: NP up: VP down: ⎡ ⎢ ⎣ node: John up: NP down: ⎤ ⎥ ⎦ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ The translation of a phrase structure tree into a recursive feature structure leaves ample room for additional attributes, e.g., phon or synsem, as used by the various schools of Nativism. Furthermore, the recursive feature structure may be recoded as a set of non-recursive feature structures, i.e., proplets. The procedure consists in recursively replacing each value consisting of a feature structure by its elementary node value, as shown below: 6.2 RECODING 6.1 AS A SET OF PROPLETS non-terminal nodes ⎡ ⎢ ⎣ node: S up: down: NP VP ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ node: NP up: S down: Julia ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ node: VP up: S down: V NP ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ node: V up: VP down: knows ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ node: NP up: VP down: John ⎤ ⎥ ⎦ terminal nodes ⎡ ⎢ ⎣ node: Julia up: NP down: ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ node: knows up: V down: ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ node: John up: NP down: ⎤ ⎥ ⎦ Formally, these proplets may be stored and retrieved in a word bank like the ones shown in Example 4.1. The mapping from phrase structure trees to recursive feature structures (e.g., 6.1) to sets of proplets (e.g., 6.2) is not symmetric, however, because there are structures which can be easily coded as a set of proplets, but have no natural representation as a phrase structure tree. This applies, for instance, to a straight line, as in the following example: 6.3 GRAPHICAL REPRESENTATION OF A LINE H I J K Such a line has no natural representation as a phrase structure tree, but it does as a set of of proplets, as in the following definition: R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 14
- 31. 6.4 RECODING THE LINE 6.3 AS A SET OF PROPLETS start ⎡ ⎢ ⎣ line: H prev: next: I ⎤ ⎥ ⎦ intermediate ⎡ ⎢ ⎣ line: I prev: H next: J ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ line: J prev: I next: K ⎤ ⎥ ⎦ finish ⎡ ⎢ ⎣ line: K prev: J next: ⎤ ⎥ ⎦ The beginning of the line is characterized by the unique proplet with an empty prev attribute, while the end is characterized by the unique proplet with an empty next attribute.8 Proplets of this kind are used in Database Semantics for the linguistic analysis of coordination. The asymmetry between the expressive power of phrase structure trees and proplets must be seen in light of the fact that the language and complexity hierarchy of substitution-based phrase structure grammar (also called the Chomsky hierarchy) is orthogonal to the language and complexity hierarchy of time-linear LA-grammar (cf. TCS’92 and FoCL’99, Part II). For example, while the formal languages ak bk and ak bk ck are in different complexity classes in phrase structure grammar, namely polynomial versus exponential, they are in the same class in LA-grammar, namely linear. Conversely, while the formal languages ak bk and HCFL are in the same complexity class in phrase structure grammar, namely polynomial, they are in different classes in LA-grammar, namely linear versus exponential. 7 Possibilities of Constructing Equivalences Regarding the use of feature structures, the most obvious difference between Nativism and Database Semantics are recursive feature structures in Nativism (cf. 1.5) and flat feature structures in Database Semantics (cf. results in 3.4 and 3.7). The recursive feature structures of Nativism are motivated by the constituent structure of the associated phrase structure trees, while the flat feature structures (proplets) of Database Semantics are motivated by the task of providing (i) a well-defined matching procedure between the language and the context level (cf. 3.3) and (ii) a time-linear storage of content in the hearer mode, a time-linear navigation in the think mode, and a time-linear production in the speaker mode (cf. 4.1). 8 Another structure unsuitable for representation as a phrase structure is a circle: I H J K There is no natural beginning and no natural end, as shown by the following definition as a set of proplets: ⎡ ⎢ ⎣ arc: H prev: K next: I ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ arc: I prev: H next: J ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ arc: J prev: I next: K ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ arc: K prev: J next: H ⎤ ⎥ ⎦ In this set, none of the proplets has an empty prev or next attribute, thus aptly characterizing the essential nature of a circle as compared to a line (cf. Example 6.4). R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 15
- 32. These differences do not in themselves preclude the possibility of equivalences between the two systems, however. Given our purpose to discover common ground, we found that phrase structure trees and the associated recursive feature structures (cf. 6.1) can be system- atically translated into equivalent sets of proplets (cf. 6.2), thus providing Nativism with a data structure originally developed for matching, indexing, storage, and retrieval in Database Semantics. Furthermore, we have seen that something like constituent structure is present in Database Semantics, namely the correlation of semantically related surfaces to the proplet from which they are realized in the speaker mode (cf. 5.1). How then should we approach the possible construction of equivalences between the two systems? From a structural point of view, there are two basic possibilities: to either look for an equivalence between corresponding components of the two systems (small solution), or to make the two candidates more equal by adding or subtracting components (large solution). Regarding a possible equivalence of corresponding components (small solution), a compar- ison is difficult. Relative to which parameters should the equivalence be defined: Complex- ity? Functionality? Grammatical insight? Data coverage? Language acquisition? Typology? Neurology? Ethology? Robotics? Some of these might be rather difficult to decide, requiring lengthy arguments which would exceed the limits of this paper. So let us see if there are some parts in one system which are missing in the other. This would provide us with the opportunity to add the component in question to the other system, thus moving inadvertently to a large solution for constructing an equivalence. Beginning with Nativism, we find the components of a universal base generated by the rules of a context-free phrase structure grammar, constrained by constituent structure, and mapped by transformations or similar mechanisms into the grammatical surfaces of the nat- ural language in question. These components have taken different forms and are propagated by different linguistic schools. Their absence in Database Semantics raises the question of how to take care of what the components of Nativism have been designed to do. Thereby, two aspects must be distinguished: (i) the characterization of wellformedness and (ii) the characterization of innateness. For Chomsky, these are inseparable because without a characterization of innateness there are too many ways to characterize wellformedness.9 For Database Semantics, in contrast, the job of characterizing syntactical and semantical wellformedness is treated as a side-effect which results naturally from a well-functioning mechanism of interpreting and producing natural language during communication. 8 Can Nativism be Turned into an Agent-oriented Approach? Next let us turn to components which are absent in Nativism.10 Their presence in DBS follows from the purpose of building a talking robot. The components, distinctions, and procedures in question are the external interfaces for recognition and action (cf. 3.1), a data structure with an associated algorithm modeling the hearer mode and the speaker mode (cf. 4.1), a systematic distinction between the language and the context level as well as their correlation in terms of matching (cf. 3.3), inferences at the context level (cf. NLC’06, Chapter 5), turn- taking, etc., all of which are necessary in addition to the grammatical component proper. Extending Nativism by adding these components raises two challenges: (i) the technical problem of connecting the historically grown phrase structure system with the new compo- 9 This problem is reminiscent of selecting the “right” phrase structure tree from a large number of possible trees (cf. 1.2), using the principle of constituent structure. 10 They are also absent in truth-conditional semantics relative to a set-theoretical model defined in a metalan- guage, which has been adopted as Nativism’s favorite method of semantic interpretation. R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 16
- 33. nents and (ii) finding a meaningful functional interaction between the original system and the new components. Regarding (i), there is the familiar problem of the missing external interfaces: how should a phrase structure system with transformations or the like be integrated into a computational model of the hearer mode and the speaker mode? Regarding (ii), it must be noted that Chom- sky and others have emphasized again and again that Nativism is not intended to model the use of language in communication. Nevertheless, an extension of Nativism to an agent-oriented system would have great theo- retical and practical advantages. For the theory, it would substantially broaden the empirical base,11 and for the practical applications, it would provide a wide range of much needed new functionalities such as procedures modeling the speaker mode and the hearer mode. Let us therefore return to the possibility of translating phrase structure trees systematically into proplets (cf. 6.1 and 6.2). Is this formal possibility enough to turn Nativism into an agent-oriented system? The answer is simple: while the translation in question is a necessary condition for providing Nativism with an effective method for matching, indexing, storage, and retrieval, it is not a sufficient condition. What is needed in addition is that the connections between the proplets (i) characterize the basic semantic relations of functor-argument structure and coordination as simply and directly as possible and (ii) support the navigation along these semantic relations in a manner which is as language-independent as possible. For these requirements, constituent structure presents two insuperable obstacles, namely (a) the proplets representing non-terminal nodes and (b) the proplets representing function words. Regarding (a), consider the set of proplets shown in 6.2 and the attempt to navigate from the terminal node Julia to the terminal node knows. Because there is no direct relation between these two proplets in 6.2, such a navigation would have to go from the terminal proplet Julia to the non-terminal proplet NP to the non-terminal proplet S to the non-terminal proplet VP to the non-terminal proplet V and finally to the terminal proplet knows. Yet eliminating these non-terminal nodes12 would destroy the essence of constituent structure as defined in 1.1 and thus the intuitive basis of Nativism. The other crucial ingredient of constituent structure, besides the non-terminal nodes, are the function words. They are important insofar as the words belonging together semantically are in large part the determiners with their nouns, the auxiliaries with their non-finite verbs, the prepositions with their noun phrases, and the conjunctions with their associated clauses. Regarding problem (b) raised by proplets representing function words, let us return to the example Suzy looked the word up, analyzed above in 1.3, 1.4, 2.2, 3.7, and 4.7. 11 As empirical proof for the existence of a universal grammar, Nativism offers language structures claimed to be learned error-free. They are explained as belonging to that part of the universal grammar which is inde- pendent from language-dependent parameter setting. Structures claimed to involve error-free learning include 1. structural dependency 2. C-command 3. subjacency 4. negative polarity items 5. that-trace deletion 6. nominal compound formation 7. control 8. auxiliary phrase ordering 9. empty category principle After careful examination of each, MacWhinney 2004 has shown that there is either not enough evidence to support the claim of error-freeness, or that the evidence shows that the claim is false, or that there are other, better explanations. 12 In order to provide for a more direct navigation, as in Example 2.1 (result). R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 17
- 34. Given that this sentence does not have a well-formed constituent structure in accordance with Definition 1.1, let us look for a way to represent it without non-terminal nodes, but with proplets for the function words the and up. Consider the following tentative proposal, which represents each terminal symbol (word) as a proplet and concatenates the proplets using the attributes previous and next, in analogy to 6.4: 8.1 TENTATIVE REPRESENTATION WITH FUNCTION WORD PROPLETS ⎡ ⎢ ⎢ ⎢ ⎣ noun: Suzy prev: next: look prn: 2 ⎤ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎣ verb: look prev: Suzy next: the prn: 2 ⎤ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎣ det: the prev: look next: word prn: 2 ⎤ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎣ noun: word prev: the next: up prn: 2 ⎤ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎣ prep: up prev: word next: prn: 2 ⎤ ⎥ ⎥ ⎥ ⎦ For the purposes of indexing, this analysis allows the storage of the proplets in – and the retrieval from – locations in a database which are not subject to any of the graphical con- straints induced by phrase structure trees, and provides for a time-linear navigation, forward and backward, from one proplet to the next.13 For a linguistic analysis within Nativism or Database Semantics, however, the analysis 8.1 is equally unsatisfactory. What is missing for Nativism is a specification of what be- longs together semantically. What is missing for Database Semantics is a specification of the functor-argument structure. For constructing an equivalence between Nativism and Database Semantics we would need to modify the attributes and their values in 8.1 as to 1. retain the proplets for the function words, 2. characterize what belongs semantically together in the surface, and 3. specify the functor-argument structure. Of these three desiderata, the third one is the most important: without functor-argument struc- ture the semantic characterization of content in Database Semantics would cease to function and the extension of Nativism to an agent-oriented approach would fail. For specifying functor-argument structure, the proplets for function words are an insupera- ble obstacle insofar as they introduce the artificial problem of choosing whether the connec- tion between a functor and an argument should be based on the function words (modifiers) or on the content words (heads). For example, should the connection between looked and the word be defined between looked and the, or between looked and word? Then there follows the question of how the connection between word and the should be defined, and how the navigation should proceed. These questions are obviated in Database Semantics by defining the grammatical relations directly between the content words. Consider the following semantic representation of Suzy looked the word up, repeating the result line of 3.7, though with the additional attribute sem to indicate the contribution of the determiner the after function word absorption: 8.2 SEMANTIC REPRESENTATION WITH FUNCTION WORD ABSORPTION ⎡ ⎢ ⎢ ⎢ ⎣ noun: Suzy sem: nm fnc: look up prn: 2 ⎤ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎣ verb: look up sem: pres arg: Suzy word prn: 2 ⎤ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎣ noun: word sem: def sg fnc: look up prn:2 ⎤ ⎥ ⎥ ⎥ ⎦ 13 The navigation would be powered by rules like that illustrated in 4.2, modified to apply to the attributes of 8.1. For a complete DBS-system handling Example 8.1, consisting of an LA-hear grammar and an LA- think/speak-grammar, see NLC’06, Section 3.6. R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 18
- 35. Acknowledgments This paper benefited from comments by Airi Salminen, University of Toronto; Kiyong Lee, Korea University; Haitao Liu, Communication University of China; and Emmanuel Giguet, Université de Caen. All remaining mistakes are those of the author. 14 For a more detailed analysis see NLC’06, Section 6.5. 15 In analogy to 2.2, the value up could also be stored as a third valency filler in the arg slot of the verb. Compared to the five proplets of Example 8.1, this analysis consists of only three. The attributes prev and next have been replaced by the attributes sem (for semantics), fnc (for the functor of a noun), and arg (for the argument(s) of a verb). The functor-argument structure of the sentence is coded by the value look up of the fnc slot of the nouns Suzy and word, and the values Suzy word of the arg slot of the verb look up (bidirectional pointering). During the time-linear LA-hear analysis, shown in 3.7, the function words are treated as full-fledged lexical items (proplets). The resulting semantic representation 8.2 provides gram- matical relations which support forward as well as backward navigation. These navigations, in turn, are the basis of the production of different language surfaces. For example, while forward navigation would be realized in English as Suzy looked the word up, the corre- sponding backward navigation would be realized as The word was looked up by Suzy.14 In 8.2, the contribution of the absorbed function word the is the value def of the cat at- tribute of the proplet word, while the contribution of the absorbed function word up is the corresponding value of the verb attribute of the proplet look up.15 Defining the grammatical relations solely between content words is motivated not only by the need to establish seman- tic relations suitable for different kinds of navigation, but also by the fact that function words are highly language-dependent, like morphological variation and word order. While Nativism and Database Semantics developed originally without feature structures, they were added later for a more detailed grammatical analysis. This paper describes the differ- ent functions of feature structures in Nativism and Database Semantics, and investigates the possible establishment of equivalences between the two systems. Establishing equivalences means overcoming apparent differences. The most basic dif- ference between Nativism and Database Semantics is that Nativism is sign-oriented while Database Semantics is agent-oriented. Ultimately, this difference may be traced to the re- spective algorithms of the two systems: the rewrite rules of PS-grammar (Nativism) do not have an external interface, while the time-linear rules of LA-grammar (Database Semantics) do. It is for this reason that Nativism cannot be extended into an agent-oriented approach, thus blocking the most promising possibility for constructing an equivalence with Database Semantics. This result complements the formal non-equivalence between the complexity hierarchies of PS-grammar and LA-grammar proven in TCS’92. The argument in this paper has been based on only two language examples, namely Julia knows John and Suzy looked the word up. For wider empirical coverage see NLC’06. There, functor-argument structure (including subordinate clauses), coordination (including gapping constructions), and coreference (including ‘donkey’ and ‘Bach-Peters’ sentences) are analyzed in the hearer and the speaker mode, based on more than 100 examples. 9 Conclusion R. Hausser / Comparing the Use of Feature Structures in Nativism and in Database Semantics 19
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- 37. Multi-Criterion Search from the Semantic Point of View (Comparing TIL and Description Logic) Marie DUŽÍ, VSB-Technical University Ostrava 17.listopadu 15 708 33 Ostrava Czech Republic Marie.Duzi@vsb.cz Peter VOJTÁŠ Charles University Prague Malostranské námČstí 25 118 00 Praha 1 Czech Republic Peter.Vojtas@mff.cuni.cz Abstract In this paper we discuss two formal models apt for a search and communication in a ‘multi-agent world’, namely TIL and EL@ . Specifying their intersection, we are able to translate and switch between them. Using their union, we extend their functionalities. The main asset of using TIL is a fine-grained rigorous analysis and specification close to natural language. The additional contribution of EL@ consists in modelling multi-criterion aspects of user preferences. Using a simple example throughout the paper, we illustrate the aspects of a multi-criterion search and communication by their analysis and specification in both the systems. The paper is an introductory study aiming at a universal logical approach to the ‘multi-agent world’, which at the same time opens new research problems and trends. 1. Introduction and motivation. In this paper we discuss two formal models that are relevant in the area of search and communication in the multi-agent world, namely Transparent Intensional Logic (TIL) and a fuzzy variant EL@ of the existential description logic EL (see [2]). Since TIL has been introduced and discussed in the EJC proceedings and EL is a well-known logical system, we are not going to introduce in details the technicalities of them. Instead, we provide just a minimal necessary introduction to keep the paper self-contained and concentrate on the analytic and specification role of these systems in the area of a semantic web search that takes into account specific user fuzzy criteria. By comparing the two formalisms we aim at providing a clue to their integration. Last but not least we’d like to illustrate the assets of a rigorous logical approach to the problem. The main asset of using TIL is a fine-grained rigorous analysis and specification close to natural language. The additional contribution of EL@ consists in modelling multi-criterion aspects of user preferences. The paper is an introductory study aiming at a universal logical approach to the ‘multi-agent world’, which at the same time opens new research problems and trends. The EL@ logic is a many-valued version of the existential description logic EL (see [2]) where fuzzification concerns only concepts and the logic is enriched with aggregation (see [21]). Specifying the intersection of TIL and EL@ , viz. the TIE@ L, we are able to translate Information Modelling and Knowledge Bases XIX H. Jaakkola et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. 21
- 38. and switch between the two systems. Using their union, TI+E@ L, we extend their functionalities. Throughout the paper we use a simple example in order to illustrate basic principles, common features, as well as differences of the two systems. Example Consider a simple communication between three agents, A, B and C. The agents can be computational, like web services, database engines, query engines, pieces of software, or even human ones. The agent A sends a message to B asking to find a hotel suitable for A (the structure of the message and the meaning of ‘suitable’ will be discussed later). After obtaining an answer the agent A chooses a hotel and sends another message to the agent C asking to seek a suitable parking place close to the chosen hotel. The criteria of A are: hotel price (e.g., as low as possible), hotel distance to a beach (should be as close as possible), hotel year of building (not too old), parking place price and parking place distance (to the hotel). We are going to describe this scenario simultaneously in two formal models: TIL (Transparent Intensional Logic) and DL (Description Logic). Of course, the model can be made more realistic by considering a larger number of agents searching for specific attribute values (this approach is motivated by Fagin in [10]). When needed, we will switch between the levels of granularity in order to go into more details. Using the DL and/or database notation we are thus going to consider agents of the type User, and the attributes Hotel_Price, Hotel_Beach_Distance, Hotel_Year_of_Construction, Parking_Price, Parking_Distance. Let the values of the attributes (results of the search) be: Particular attribute preferences of a user U can be evaluated by assigning the preference degree, a real number in the interval [0,1], to the attribute values. For instance, cheap_U(150) = 0.75, close_U (300) = 0.6, new_U (1980) = 0.2, and similarly for the other values. In this way we obtain fuzzy subsets cheap_U, close_U, new_U of the attribute domains, which can be recorded in a fuzzy database operation table (see [15]): Our reasoning and decision making is driven not only by the preferences we assign to the values of attributes, but also by the weight we assign to the very criteria of interest. For instance, when being short of money, the low price of the hotel is much more important than its closeness to the beach. When being rich we may prefer a modern high-tech equipped hotel situated on the beach. On the other hand a hotel close to the beach may become totally unattractive in a tsunami-affected area. The multi-criterion decision is thus seldom based on a simple conjunctive or disjunctive combination of the respective factors, and we need an algorithm to compute global user preferences as a composition of particular weighted fuzzy values of the selection criteria. The algorithm can be rather sophisticated. However, for the sake of simplicity, let it be just a weighted average: M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 22
- 39. 6 _ _ 3 _ 2 ) _ , _ , ( @ U new U close U cheap U new U close U cheap U Computing the global degree of preferences of the hotel h1 for the user U, we obtain: ... 58 . 0 6 5 . 3 6 2 . 0 6 . 0 3 75 . 0 2 ) 2 . 0 , 6 . 0 , 75 . 0 ( @ U Since this value is higher than the value of the hotel h2, the user U is going to choose h1. Of course, another user can have different preferences, and also the preferences of one and the same user may dynamically change in time. Besides the fact that in a multi-agent world we work with vague, fuzzy or uncertain information, we have to take into account also the demand on robustness and distribution of the system. The system has to be fully distributive, and we have to deal with value gaps because particular agents may fail to supply the requested data. On the other hand, in critical and emergency situations, which tend to a chaotic behaviour, the need for an adequate data becomes a crucial point. Therefore the classical systems which are based on the Closed World Assumption are not plausible here. We have to work under the Open World Assumption (OWA), and a lack of knowledge must not yield a collapse of the system. For instance, it may happen that we are not able to retrieve the distance of the hotel h1 to the beach, and the available data are as follows: There are several possibilities of dealing with lacking data. We may use default values (e.g., average, the best or the worst ones), or treat the missing values as value gaps of partial functions. From the formal point of view, TIL is a hyper-intensional partial O-calculus. By ‘hyper-intensional’ we mean the fact that the terms of the ‘language of TIL constructions’ are not interpreted as the denoted functions, but as algorithmically structured procedures, known as TIL constructions, producing the denoted functions as outputs. Thus we can rigorously and naturally handle the terms that are in classical logics ‘non-denoting’, or undefined;1 in TIL each term is denoting a full-right entity, namely a construction. Hence (well-typed) terms never lack semantics. It may just happen (in well defined cases) that the denoted procedure fails to produce an output function. And if it does not fail it may happen that the produced function fails to have a value at an argument. These features of TIL are naturally combined with and completed by the EL@ fuzzy tools, in particular the aggregation algorithms. The paper is organized as follows: Chapter 2 contains brief introductory remarks on TIL. Chapter 3 introduces the EL@ description logic, and Chapter 4 is devoted to the formal description of our motivating examples, which gives us a flavour of the common features of both the models. As a result, in concluding Chapter 5 we outline a possible hybrid system and specify the trends of future research. 1 For the logic of definedness see [11]. M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 23
- 40. 2 TIL in brief. In this Chapter we provide just a brief introductory explanation of the main notions of Transparent Intensional Logic (TIL). For exact definitions and details see, e.g., [5], [7], [8], [19], [20]. TIL approach to knowledge representation can be characterised as the ‘top-down approach’. TIL ‘generalises to the hardest case’ and obtains the ‘less hard cases’ by lifting various restrictions that apply only higher up. This way of proceeding is opposite to how semantic theories tend to be built up. The standard approach consists in beginning with atomic sentences, then proceeding to molecular sentences formed by means of truth- functional connectives or by quantifiers, and from there to sentences containing modal operators and, finally, attitudinal operators. Thus, to use a simple case for illustration, once a vocabulary and rules of formation have been laid down, a semantics gets off the ground by analysing an atomic sentence as follows: (1) “Charles selected the hotel h”: S(a,h) And further upwards: (2) “Charles selected the hotel h, and Thelma is happy”: S(a,h) š H(b) (3) “Somebody selected the hotel h”: x S(x,h) (4) “Possibly, Charles selected the hotel h”: ‘ S(a,h) (5) “Thelma believes that Charles selected the hotel h”: B(b,S(a,h)). In non-hyperintensional (i.e., non-procedural) theories of formal semantics, attitudinal operators are swallowed by the modal ones. But when they are not, we have three levels of granularity: the coarse level of truth-values, the fine-grained level of truth-conditions (propositions, truth-values-in-intension), and the very fine-grained level of hyper- propositions, i.e., constructions of propositions. TIL operates with these three levels of granularity. We start out by analysing sentences from the uppermost end, furnishing them with a hyperintensional2 semantics, and working our way downwards, furnishing even the lowest-end sentences (and other empirical expressions) with a hyperintensional semantics. That is, the sense of a sentence such as “Charles selected the hotel h” is a hyper-proposition, namely the construction of the denoted proposition (i.e., the instruction how to evaluate the truth-conditions of the sentence in any state of affairs). When assigning a construction to an expression as its meaning, we specify a procedural know-how, which must not be confused with the respective performatory know-how. Distinguishing performatory know-how from procedural know-how, the latter could be characterised “that a knower x knows how A is done in the sense that x can spell out instructions for doing A.”3 For instance, to know what Goldbach Conjecture means is to understand the instruction to find whether ‘all positive even integers • 4 can be expressed as the sum of two primes’. It does not include either actually finding out (whether it is true or not by following a procedure or by luck) or possessing the skill to do so.4 Furthermore, the sentence “Charles selected the hotel h” is an ‘intensional context’, in the sense that its logical analysis must involve reference to empirical parameters, in this case both possible worlds and instants of time. Charles only contingently selected the hotel; i.e., he did so only at some worlds and only sometimes. The other reason is because the analysans must 2 The term ‘hyperintensional’ has been introduced by Max Cresswell, see [4]. 3 See [16, p.6] 4 For details on TIL handling knowledge see [8]. M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 24
- 41. be capable of figuring as an argument for functions whose domain are propositions rather than truth-values. Construing ‘S(a,h)’ as a name of a truth-value works only in the case of (1) and (2). It won’t work in (5), since truth-values are not the sort of thing that can be believed. Nor will it work in (4), since truth-values are not the sort of thing that can be possible. Constructions are procedures, or instructions, specifying how to arrive at less-structured entities. Being procedures, constructions are structured from the algorithmic point of view, unlike set-theoretical objects. The TIL ‘language of constructions’ is a modified hyper- intensional version of the typed O-calculus, where Montague-like O-terms denote, not the functions constructed, but the constructions themselves. Constructions qua procedures operate on input objects (of any type, even on constructions of any order) and yield as output (or, in well defined cases fail to yield) objects of any type; in this way constructions construct partial functions, and functions, rather than relations, are basic objects of our ontology. The choice of types and of constructions is not given once for ever: it depends on the area to be analyzed. By claiming that constructions are algorithmically structured, we mean the following: a construction Cbeing an instructionconsists of particular steps, i.e., sub-instructions (or, constituents) that have to be executed in order to execute C. The concrete/abstract objects an instruction operates on are not its constituents, they are just mentioned. Hence objects have to be supplied by another (albeit trivial) construction. The constructions themselves may also be only mentioned: therefore one should not conflate using constructions as constituents of composed constructions and mentioning constructions that enter as input into composed constructions, so we have to strictly distinguish between using and mentioning constructions. Just briefly: Mentioning is, in principle, achieved by using atomic constructions. A construction is atomic if it is a procedure that does not contain any other construction as a used subconstruction (a constituent). There are two atomic constructions that supply objects (of any type) on which complex constructions operate: variables and trivializations. Variables are constructions that construct an object dependently on valuation: they v- construct, where v is the parameter of valuations. When X is an object (including constructions) of any type, the Trivialization of X, denoted 0 X, constructs X without the mediation of any other construction. 0 X is the atomic concept of X: it is the primitive, non- perspectival mode of presentation of X. There are two compound constructions, which consist of other constructions: Composition and Closure. Composition is the procedure of applying a function f to an argument A, i.e., the instruction to apply f to A to obtain the value (if any) of f at A. Closure is the procedure of constructing a function by abstracting over variables, i.e., the instruction to do so. Finally, higher-order constructions can be used twice over as constituents of composed constructions. This is achieved by a fifth construction called Double Execution. 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 entities unstructured from the algorithmic point of view belonging to a type of order 1. Given a so-called epistemic (or ‘objectual’) base of atomic types (R-truth values, L- individuals, W-time moments / real numbers, Z-possible worlds), mereological complexity is increased by the induction rule for forming partial functions: 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 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 to be analysed. M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 25
- 42. Constructions that construct entities of order 1 are constructions of order 1. They belong to a type of order 2, denoted by *1. This type *1 together with atomic types of order 1 serves as a base for the induction rule: any collection of partial functions, 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 functions involving such constructions, belong to a type of order 3. And so on ad infinitum. Definition (Constructions) i) Variables x, y, z, …are constructions that construct objects of the respective types dependently on valuations v; they v-construct. ii) Trivialization: Where X is an object whatsoever (an extension, an intension or a construction), 0 X is a construction called trivialization. It constructs X without any change. iii) Composition: If X v-constructs a function F of a type (D E1…Em), and Y1,…,Ym v-construct entities B1,…,Bm of types E1,…,Em, respectively, then the composition [X Y1 … Ym] is a construction that v-constructs the value (an entity, if any, of type D) of the (partial) function F on the argument ¢B1, …, Bn². Otherwise the composition [X Y1 … Ym] does not v-construct anything: it is v-improper. iv) Closure: If x1, x2, …,xm are pairwise distinct variables that v-construct entities of types E1, E2, …, Em, respectively, and Y is a construction that v-constructs an entity of type D, then [Ox1…xm Y] is a construction called closure, which v-constructs the following function F of the type (D E1…Em), mapping E1 u…u Em to D: Let B1,…,Bm be entities of types ȕ1,…,ȕm, respectively, and let v(B1/x1,…,Bm/xm) be a valuation differing from v at most in associating the variables x1,…xm with B1,…,Bm, respectively. Then F associates with the m-tuple ¢B1,…,Bm² the value v(B1/x1,…,Bm/xm)-constructed by Y. If Y is v(B1/x1,…,Bm/xm)- improper (see iii), then F is undefined on ¢B1,…,Bm². v) Double execution: If X is a construction that v-constructs a construction X’, then 2 X is a construction called double execution. It v-constructs the entity (if any) v-constructed by X’. Otherwise the double execution 2 X is v-improper. vi) Nothing is a construction, unless it so follows from i) through vi). The notion of construction is a notion that is the most misunderstood notion of those ones used in TIL. Some logicians ask: Are constructions formulae of type-logic? Our answer: No! Another question: Are they denotations of closed formulae? Our answer: No! So a pre-formal, ‘pre-theoretical’ characteristics is needed: constructions are abstract procedures. Question: Procedures are time-consuming, how can they be abstract? Answer: The realization of an algorithm is time-consuming, the algorithm itself is timeless and spaceless. Question: So what about your symbolic language? Why do you not simply say that its expressions are constructions? Answer: These expressions cannot construct anything they serve only to represent (or encode) constructions. Question: But you could do it like Montague6 did: To translate expressions of natural language into the language of intensional logic, and then interpret the result in the standard manner. What you achieve using ‘constructions’ you would get using metalanguage. Answer(s): First, Montague and other intensional logics interpret terms of their language as the respective functions, i.e., set-theoretical mappings. However, these mappings are the outputs of executing the respective procedures. Montague does not make it possible to mention the 6 For details on Montague system see, e.g., [12, pp. 117-220]. M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 26
- 43. procedures as objects sui generis, and to make thus a semantic shift to hyperintensions. Yet we do need a hyperintensional semantics. Notoriously well-known are attitudinal sentences which no intensional semantics can properly handle, because its finest individuation is equivalence.7 Second, our logic is universal: we do not need to work as part-time linguisticians. Using the ‘language of constructions’ we directly encode constructions. Definition ((D-)intension, (D-)extension) (D-)intensions are members of a type (DZ), i.e., functions from possible worlds to the arbitrary type D. (D-)extensions are members of the type D, where D is not equal to (EZ) for any E, i.e., extensions are not functions from possible worlds. Remark on notational conventions: An object A of a type D is called an D-object, denoted A/D. That a construction C v-constructs an D-object is denoted C ov D. We will often write ‘x A’, ‘x A’ instead of ‘[0 D Ox A]’, ‘[0 D Ox A]’, respectively, when no confusion can arise. We also often use an infix notation without trivialisation when using constructions of truth- value functions š (conjunction), › (disjunction), Š (implication), { (equivalence) and negation (™), and when using a construction of an identity. 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). We will use variables w, w1, w2,… as v-constructing elements of type Z (possible worlds), and t, t1, t2, … as v-constructing elements of type W (times). If C o DWZ v-constructs an D-intension, the frequently used composition of a form [[C w] t], v-constructing the intensional descent of the D-intension, will be abbreviated as Cwt. Some important kinds of intensions are: Propositions, type RWZ. They are denoted by empirical (declarative) sentences. Properties of members of a type D, or simply Į-properties, type (RD)WZ.8 General terms (some substantives, intransitive verbs) denote properties, mostly of individuals. Relations-in-intension, type (RE1…Em)WZ. For example transitive empirical verbs, also attitudinal verbs denote these relations. Omitting WZ we get the type (RE1…Em) of relations-in- extension (to be met mainly in mathematics). D-roles, offices, type DWZ, where D (RE). Frequently LWZ. Often denoted by concatenation of a superlative and a noun (“the highest mountain”). Individual roles correspond to what Church in [3] called “individual concept”. The role of the above defined constructions in a communication between agents will be illustrated in Chapter 4, in particular in Paragraph 4.5. Just a note to elucidate the role of Trivialisation and empirical parameters w o Z, t o W: The TIL language is not based on a fixed alphabet: the role of formal constants is here played by Trivialisations of non- constructional entities, i.e., the atomic concepts of them. Each agent has to be equipped with a basic ontology, namely the set of atomic concepts he knows. Thus the upper index ‘0 ’ serves as a marker of the atomic concept (like a ‘key-word’) that the agent should know. If they do not, they have to learn it. The lower index ‘wt’ can be understood as an instruction to execute an empirical inquiry (search) in order to obtain the actual current value of an intension, for instance by searching agent’s database or by asking the other agents, or even by means of agent’s sense perception. 7 See [12, p.73] 8 Collections, sets, classes of ‘D-objects’ are members of type (RD); TIL handles classes (subsets of a type) as characteristic functions. Similarly relations (-in-extension) are of type(s) (Rȕ1…ȕm). M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 27
- 44. 3 The EL@ description logic In a multi-agent world like the semantic web we need to retrieve, process, share or reuse information which is often vague or uncertain. The applications have to work with procedures that deal with the degree of relatedness, similarity or ranking. These motivations lead to the development of the fuzzy description logic (see, [18]). In this chapter we briefly describe a variant of the fuzzy description logic, namely EL@ (see [21]). One of the principal sources of fuzziness is user evaluation (preference) of crisp values of attributes. For instance, the hotel price is crisp but user evaluation may lead to a fuzzy predicate like a cheap, moderate, or expensive hotel. User preferences are modelled by linearly ordered set of degrees T = [0,1] extending classical truth-values. Thus we have: 0 = False = A = the worst T and 1 = True = T = the best T Now when searching a suitable object we have to order the set of available objects according to the user degrees assigned to object-attribute values. Practical experiences have shown that the ordering is seldom based on a conjunctive or disjunctive combination of particular scores. Rather, we need to work with a fuzzy aggregation function that combines generally incomparable sets of values. The EL@ logic is in some aspects a weakening of Straccia fuzzy description logic and in some other aspects a strengthening.9 The restrictions concern using just crisp roles and not using negation. Moreover, quantification is restricted to existential quantifiers. The extension concerns the application of aggregation functions. Thus we loose the ability to describe fuzziness in roles but gain the ability to compute a global user score. The EL@ alphabet consists of (mutually disjoint) sets NC of concept names containing T, NR role names, NI instance names and constructors containing and a finite set C of combination functions with an arity function ar : C Æ {n N : n • 2}. Concept descriptions in EL@ are formed according to the following syntax rules (where @C) The interpretation structures of our description logic EL@ are parameterized by an ordered set of truth-values T (the degrees of membership to a domain of a fuzzy concept) and a set of n- ary aggregation functions over T. An interpretation structure T is thus an algebra T = {T, •, {@•T: @ C }}, where (T , •,T ) is an upper complete semilattice with the top element T, and @•T: Tar(@) Æ T is a lattice of totally continuous (order-preserving) aggregation functions. A T –interpretation is then a pair I = ¢ǻI , •I ², with a nonempty domain ǻI and the interpretation of language elements aI ǻI , for a NI AI : ǻI Æ T, for A NC (concepts can be fuzzy, like a suitable hotel) rI Ž ǻI × ǻI , for r NR 9 For details on fuzzy description logic see [18]. M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 28
- 45. (Roles remain crisp; however, users may interpret these data in a fuzzy way. We assume that fuzziness should not be attached to the data from the very beginning). The extension of the T –interpretation I to the composed EL@ concepts is given by (@(C1, …, Cn))I (x) = @•(CI 1 (x), …, CI n (x)) and (r.C)I (x) = sup{CI (y): (x, y) rI } The EL@ is a surprisingly expressive language with good mathematical properties. It opens a possibility to define declarative as well as procedural semantics of an answer to a user query formulated by means of a fuzzy concept definition. The discussion on the complexity of particular problems, like satisfiability, the instance problem, the problem of deciding subsumption and the proof of soundness and completeness are, however, out of scope of the present paper. For details, see, e.g., [21]. 4 TIL and EL@ combined. Using the example from the outset we are now going to outline the way of integrating the two systems. We illustrate the work with a typed and / or non-typed language, and the role of basic pre-concepts like a type, domain, concept and role. As stated above, TIL is a typed system. The basic types serve as the pre-concepts. 4.1 Pre-concepts a) Basic types (TIL): The epistemic base is a collection of: R – the set of truth-values {T, F}, L – the universe of discourse (the set of individuals), W – the set of times (temporal factor) and / or real numbers, Z – the set of possible worlds (modal factor) (EL@ ): Basic pre-concepts are T and ǻI , as specified in Chapter 3. The description logic does not work explicitly with the temporal and modal factor. However, there is a possibility to distinguish between necessary ex definitione (T-boxes) and contingency of attribute values (A-boxes). Moreover, EL@ contributes the means for handling user preference structures – the preference factor. (TIL): The universe of discourse is the (universal) set of individuals. EL@ works with varying domains of interpretation ǻI . b) Functions and relations TIL is a functional system: Composed (functional) types are collections of partial functions; D-sets and (DE)-relations are modelled by their characteristic functions, objects of types (RD), (RDE), respectively. (EL@ ): Being a variant of description logic, EL@ is based on the first-order predicate logic where n-ary predicates are interpreted as n-ary relations over the universe. However, in EL@ this is true only for n = 2: binary predicates are crisp roles. In the other aspects EL@ is actually functional; it deals with (crisp) n-ary aggregation functions, and unary predicates (concepts) are interpreted as fuzzy sets by their fuzzy characteristic functions ǻI Æ T. M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 29
- 46. 4.2 Assortment of the individuals in the universe (TIL) properties In order to classify individuals into particular sorts, we use properties of individuals. They are intensions, namely functions that depending on the states of affairs (the modal parameter Z) and time (the parameter W) yield a population of individuals (RL) that actually and currently have the property in question. Example: h1, h2, h3 / L are individuals with the property Hotel / (RL)WZ of being a hotel. In the database setting these individuals belong to the domain of the attribute “hotel”, or, these individuals may instantiate the entity set HOTEL. That h1, h2, h3 are hotels is in TIL represented by the constructions of the respective propositions OwOt [0 Hotelwt 0 h1], OwOt [0 Hotelwt 0 h2], OwOt [0 Hotelwt 0 h3], where the property Hotel / (RL)WZ is first intensionally descended (0 Hotelwt) and then ascribed to an individual: [0 Hotelwt 0 hi]. Finally, to complete the meaning of ‘hi is a hotel’, we have to abstract over the modal and temporal parameter in order to construct a proposition of type RWZ that hi is a hotel: OwOt [0 Hotelwt 0 hi]. Gloss the construction as an instruction for evaluating the truth-conditions: In any state of affairs of evaluation (OwOt) check whether the individual (0 hi) currently belongs to the actual population of hotels ([0 Hotelwt 0 hi]). (EL@ ) equivalents. Names of properties correspond to the elements of NC and NR. The above propositions are represented by membership assertions: Hotel(h1), Hotel(h2), Hotel(h3). The example continued. Let A, B, C / L are individuals with the property of being an agent. In the database setting these individuals belong to the domain of the attribute “user”, or, these individuals may instantiate the entity set AGENT. However, in order to be able to represent n- ary properties of individuals by means of binary ones, we need to identify particular users. Of course, in case of a big and varying set of users it is not in general possible to identify each user, and we often have to consider (a smaller number of) user profiles. (TIL): That A, B, C are agents is represented by the constructions of the respective propositions: OwOt [0 Agentwt 0 A], OwOt [0 Agentwt 0 B], OwOt [0 Agentwt 0 C], where the property Agent / (RL)WZ is intensionally descended and then ascribed to an individual: [0 Agentwt 0 Ai]. Finally, in order to construct a proposition, we have to abstract over the parameters w, t: OwOt [0 Agentwt 0 Ai]. Gloss: In any state of affairs of evaluation check whether the individual A currently belongs to the actual population of agents. (EL@ ): The above propositions are represented by membership assertions: Agent(A), Agent(B), Agent(C). (TIL): Parking / (RL)WZ; the property of an individual of being a parking place. For instance, the proposition that p1, p2, …, pn / L are individuals with the property of being a parking place, is constructed by M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 30
- 47. OwOt [0 Parkingwt 0 pi]. (EL@ ): These individuals belong to the extension of the concept: Parking(pi). 4.3 Attributes – criteria In general, attributes are empirical functions, i.e. intensions of a type (Įȕ)WZ. For instance, ‘the President of (something)’ denotes a (singular) attribute. Dependently on the modal factor Z and time W the function in question associates the respective country with the unique individual playing the role of its President. But, for instance, George W. Bush might not have been the President of the USA (the modal dependence), and he has not always been and will soon not be10 the President (the temporal dependence). (TIL) Price / (WL)WZ; an empirical function associating an individual (of type L) with a W- number (its price); to obtain a price of a hotel hi, we have to execute an empirical procedure: OwOt [0 Pricewt 0 hi]. (EL@ ) the value of the attribute Price can be obtained, e.g., by an SQL query SELECT Price FROM Hotel WHERE Hotel.Name=hi or by using a crisp atomic role hotel_price. (TIL) Distance / (WLL)WZ; an empirical function assigning a W-number (the distance) to a pair of individuals, for instance: OwOt [0 Distancewt 0 hi 0 pi]. (TIL) DistE / (WL)WZ; the empirical function assigning to an individual a W-number (its distance to another chosen entity E – a beach, a hotel, …). (EL@ ) Database point of view: Assuming we have a schema Distance(Source, Target, Value), this is the value of the attribute Distance.Value. It can be obtained, e.g., by the SQL query SELECT Distance.Value FROM Distance, Hotel WHERE Hotel.Name=hi AND Hotel.Address=x AND Distance.Source=x AND Distance.Target=E DL point of view: In DL we meet a problem here, because the relation Distance is of arity 3 and DL is a binary conceptual model. For each individual E we can consider an atomic role hotel_distance_from_E. (Of course, in practical applications we can combine these approaches). (TIL) Year / (WL)WZ; an empirical function assigning to an individual a W-number (its year of building). (EL@ ) Database and DL points of view similar as above (TIL) Appertain-to / (R LL)WZ; the binary relation between individuals. For example, a parking place pi belonging to a hotel hi: OwOt [[0 Parkingwt 0 pi] š [0 Hotelwt 0 hi] š [0 Appertain-towt 0 hi 0 pi]]. (EL@ ) the relation between a particular hotel and a parking; a crisp role 10 Written in January 2007 M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 31
- 48. 4.4 Evaluation of criteria by combining user preferences The procedural semantics of TIL makes it possible to easily model the way particular agents can learn by experience. An agent may begin with a small ontology of atomic primitive concepts (trivialisations of entities) and gradually obtain pieces of information on more detailed definitions of the entities. In TIL terminology each composed construction yielding an entity E is an ontological definition of E. For instance, the agent A may specify the property of being a Suitable (for-A) hotel by restricting the property Hotel. To this end the property Suitable hotel is defined by the construction composing the price, distance and year attribute values and yielding the degree greater than 0.5. (TIL): Suitable-for / ((RL)WZ L (RL)WZ)WZ – an empirical (parameters W, Z) function that applied to an individual (of type L) and a property (of type (RL)WZ) returns a property (of type (RL)WZ). For instance, the property of being a suitable hotel for the agent A can be defined by: OwOt [0 Suitable-forwt 0 A 0 Hotel] = OwOt Ox [[0 Hotelwt x] š [[0 Evaluatewt 0 A [0 Pricewt x] [0 DistEwt x] [0 Yearwt x]] t 0.5]]. By way of further refining, we can again define the atomic concept 0 Evaluate. To this end we enrich the ontology by 0 Aggregate and 0 Apt-for, which can again be refined. And so on, theoretically ad infinitum. Evaluate / (W L WWW)WZ - an empirical function that applied to an individual a and a triple of W- parameters (e.g., price, distance, year) returns a W-number [0,1], which is the preference degree of a particular hotel for the agent a. [0 Evaluatewt a par1 par2 par3] = [0 Aggregate [0 Apt-forwt a par1] [0 Apt-forwt a par2] [0 Apt-forwt a par3]]. Aggregate / (W WWW) – the aggregation function that applied to the triple of W-numbers returns a W-number = the degree of appropriateness. Apt-for / (W LW) – an empirical function that applied to an individual a / L and a W- parameter pari (e.g., price, distance, and so like) returns a preference scale of the respective parameter pari for the user a. The scale is a W-number [0,1]. For instance, [0 Evaluatewt 0 A [0 Pricewt x] [0 DistEwt x] [0 Yearwt x]] = [0 Aggregate [0 Apt-forwt A [0 Pricewt x]] [0 Apt-forwt A [0 DistEwt x]] [0 Apt-forwt A [0 Yearwt x]]]. The empirical function Evaluate is the key function here. Applied to an individual agent (user) and particular criteria it returns the agent’s preference-degree of a particular object. Each agent may dynamically (parameter W) choose (parameter Z) its own function Evaluate. The algorithm computing the preference-degree of an object consists of two independent sub- procedures: i) user preference scale Apt-forwt of the TIL-type (W LW), or using the EL@ notation: ¢user, pari² o [0,1], where pari is the value of a particular criterion (for instance price, distance, etc.). Here the additional role of EL@ comes into play. The EL@ logic makes it possible to choose an appropriate scale algorithm. It can be a specific function for a particular user U1, e.g.: M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 32
- 49. ii) the aggregation function Aggregate of the TIL -type (W WWW), or in the EL@ notation (understood as a many valued connective) @: [0,1]3 o [0,1], computing the global preference degree. Here we consider the Aggregate function as not being user-dependent, but rather system-dependent (therefore, in TIL –notation there is no WZ-parameter). In other words, it is a system algorithm of computing the general user preference. Of course, we might let each user specify his/her/its own algorithm but in practice it suffices to consider different user profiles associated with each aggregation function. Thus the system may test several algorithms of aggregation, e.g., those that were used for users with a similar profile, in order to choose the suitable aggregation. It does not seem to be necessary to further refine the specification in TIL. Instead we either call at this point a software module, or make use of the EL@ logic. In the example above we used the weighted average: 4.5 Communication of agents; messages The communication aspects are not elaborated in EL@ from the semantic point of view. Hence it represents the added value of TIL when integrating with EL@ . However, in SQL we have ORDER BY command and when dealing with preferences we work with the notion of the best, top-k, respectively, answers. The EL@ many valued logic setting understood as a comparative tool (numerical values do not matter) is an appropriate tool for evaluating fuzzy predicates. It provides a good semantics for ordering preferences of answers (see [13]). The TIL-philosophy is driven by the fact that natural language is a perfect logical language. Hence the TIL-specification is close to an ordinary human reasoning and natural-language communication. On the other hand, however, the high expressive power of the TIL language of constructions may sometimes be an obstacle to an effective implementation. This problem is dealt with by the step-by-step refinement as discussed above. At the first step we specify just a coarse-grained logical form of a message; the execution is left to particular Java modules. Then a more fine-grained specification makes it possible to increase agent’s “intelligence” by letting him dynamically decide which finer software modules should be called. To this end we combine Java modules, Prolog, fuzzy Prolog Ciao, etc. (TIL): The general scheme of a message is: Message / (R L L RWZ)WZ OwOt [0 Messagewt 0 Who 0 Whom OwOt [0 Typewt 0 What]], where M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 33
- 50. Who /L, Whom /L, What (content)/ĮWZ, Type / (RĮWZ)WZ, What – the subject of the message is a specification of an intension (usually a proposition of type RWZ). (EL@ ): The description logic does not incorporate a specific semantic logical description of messages. It is usually handled by an implementation component (generally in the Software Engineering part) by dealing with exceptions, deadlocks, etc. (TIL): There are three basic types of messages that concern propositions; i.e., these types are properties of propositions, namely Order, Inform, Query/(RRWZ)WZ. In an ordinary communication act we implicitly use the type Inform affirming that the respective proposition is true. But using an interrogative sentence we ask whether the proposition is true (Query), or using an imperative sentence we wish that the proposition were true (Order). The content of a message is then the construction of a proposition, the scheme of which is given by: OwOt [0 Typewt 0 What] o RWZ. In what follows we specify in more details possible typical types of messages. Type = {Seek, Query(Yes-No), Answer, Order, Inform, Unrecognised, Refine,…}; where Typei / (RDWZ)WZ or Typei / (R n)WZ. Examples of a content of a message: [0 Seekwt 0 What]; What / DWZ o send me an answer = the actual D-value of What in a given state of affairs w,t of evaluation. [0 Querywt 0 What]; What / RWZ o send me an answer = the actual R-truth-value of What in a given state of affairs w,t. [0 Orderwt 0 What]; What / RWZ o manage What to be actually True (in a state of affairs w,t.) [0 Informwt 0 What]; What / RWZ o informing that What is actually True [[0 Answerwt 0 What] = a / D]; where a = [0 Whatwt]; the answer to a preceding query or seek. [0 Unrecognisedwt 00 What]; the atomic concept 0 What has not been recognised; a request for refinement. Note that Unrecognised is of type (R n)WZ, the property of a construction (usually an atomic concept). Therefore the content of the message is not the intension What constructed by 0 What, but the construction 0 What itself. The latter is mentioned here by trivialisation, therefore 00 What. [[0 Refinewt 00 What] = 0 C o DWZ]; an answer to the message on unrecognised atomic concept. The construction C is the respective composed specification (definition) of What, i.e., C and 0 What are equivalent, they construct the same entity: C = 0 What. For instance, the set of prime numbers can be defined as the set of numbers with two factors: [[0 Refinewt 00 Prime] = 0 [Ox [0 Card Oy [0 Div x y] = 0 2]]], where x, y o Nat (the type of natural numbers), Div / (R Nat Nat) – the relation of being divisible by, Card / (Nat (R Nat))– the number of elements of a set. M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 34
- 51. 4.6 Example of communication Now we continue the simple example from the outset. We will analyse a part of the dialog of the three agents A, B, C. Sentences will be first written in ordinary English then analysed using TIL, transformed into the standardised message, and if needed provided by a gloss. For the sake of simplicity we will omit the specification of TIL-types of particular objects contained in a message. However, since the TIL-type is an inseparable part of the respective TIL-construction, we do not omit it in a real communication of agents. For instance, when building an agent’s ontology, each concept is inserted with its typing. Message 1 (A to B): ‘I wish B to seek a suitable hotel for me.’ A(TIL): OwOt [0 Wishwt 0 A OwOt [0 Seekwt 0 B [0 Suitable-forwt 0 A 0 Hotel]]], Wish/(RLRWZ)WZ, Seek/(RL(RL)WZ)WZ, A(TIL m1): OwOt [0 Messagewt 0 A 0 B OwOt [0 Seekwt [0 Suitable-forwt 0 A 0 Hotel]]] Gloss: The agent A is sending a message to B asking to seek a suitable hotel for A. Message 2 (B to A): However, the agent B does not understand the sub-instruction [0 Suitable-forwt 0 A 0 Hotel], because he does not have the atomic concept 0 Suitable-for in his ontology. Therefore, he replies a message to A, asking to explain: ‘I did not recognise 0 Suitable-for.’ B(TIL m2): OwOt [0 Messagewt 0 B 0 A OwOt [0 Unrecognisedwt 00 Suitable-for] Remark Thus the lower index wt can be understood as an instruction to execute an empirical inquiry (search) in order to obtain the actual current value of an intension, here the property of being a suitable hotel (for instance by searching agent’s database or by asking the other agents, or even by means of agent’s sense perception). The upper index 0 serves as a marker of the primitive (atomic) concept belonging the agent’s ontology. If it does not, i.e., if the agent does not know the concept, he has to ask the others in order to learn by experience. Message 3 (A to B): The agent A replies by specifying the restriction of the property Hotel to those hotels which are evaluated with respect to price, distance and the year of building with the degree higher than 0.5: A(TIL) 0 Suitable-for / ((RL)WZ L (RL)WZ)WZ, a o L, p o (RL)WZ; 0 Suitable-for = OwOt Oap OwOt Ox [[pwt x] š [[0 Evaluateh wt a [0 Pricewt x] [0 DistEwt x] [0 Yearwt x]] t 0 0.5]]. Gloss: The A’s answer message should refine the atomic concept 0 Suitable-for. Now there is a problem, however. The agent B would have to remember the respective message asking for the refinement in order to apply the property to proper arguments (namely A and Hotel). This would not be plausible in practice, because A is the aid prayer, not B. Therefore the answer message contains the smallest constituent containing the refined concept: A(TIL m3): OwOt [0 Messagewt 0 A 0 B OwOt [0 Refinewt 0 [0 Suitable-forwt 0 A 0 Hotel] = 0 [OwOt Ox [[0 Hotelwt x] š [[0 Evaluateh wt 0 A [0 Pricewt x] [0 DistEwt x] [0 Yearwt x]] t 0.5]]]]] M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 35
- 52. In this way the agent B obtains a piece of knowledge what should he look for. Another possibility would be A’s sending the original message 1 refined, i.e., the constituent [0 Suitable-forwt 0 A 0 Hotel] replaced by the new specification: A(TIL m3’): OwOt [0 Messagewt 0 A 0 B OwOt [0 Seekwt OwOt Ox [[0 Hotelwt x] š [[0 Evaluateh wt 0 A [0 Pricewt x] [0 DistEwt x] [0 Yearwt x]] t 0.5]]]] However, we prefer the former, because in this way B learned what a suitable hotel for A means. Or rather, he would learn if he understood 0 Evaluateh , which may not be the case if he received the request for the first time. Thus if B does not have the concept in his /her ontology, he again sends a message asking for explaining: Message 4 (B to A): B: I did not recognise 0 Evaluateh . B(TIL m4): OwOt [0 Messagewt 0 B 0 A OwOt [0 Unrecognisedwt 00 Evaluateh ] Message 5 (A to B): A(TIL m5): OwOt [0 Messagewt 0 A 0 B OwOt [0 Refinewt 0 [0 Evaluatewt 0 A [0 Pricewt x] [0 DistEwt x] [0 Yearwt x]] = = 0 [0 Aggregate [0 Apt-forwt A [0 Pricewt x]] [0 Apt-forwt A [0 DistEwt x]] [0 Apt-forwt A [0 Yearwt x]]] And so on, the refinement may continue and the agents may learn new concepts (from the theoretical point of view ad infinitum). Anyway, finally B fully understands the message and attempts at fulfilling the task; recall that he is to seek a suitable hotel for A. Note that the whole process is dynamic, even agents’ learning by the process of refining particular atomic concepts. B knows now that actually and currently a hotel suitable for A is such a hotel the price, distance from the beach and the year of building of which evaluate with respect to A’s scaling [0 Apt-forwt 0 A] with the degree higher than 0.5. But he also knows that it might have been otherwise (the modal parameter w / Z) and it will not have to be always so (the temporal parameter t / W). In other words, A and B now share common knowledge of the composed concept defining the property of being a suitable hotel for A. When eventually B accomplishes his search he sends an answer to A: Message 6 (B to A): A(TIL m6): OwOt [0 Messagewt 0 B 0 A OwOt [0 Answerwt [0 Suitable-forwt 0 A 0 Hotel] = {¢h1,0.7²,{¢h5,0.53²}] 11 Gloss: B found out that there are two instances of the property v-constructed by the construction [0 Suitable-forwt 0 A 0 Hotel], namely the hotel h1 that has been evaluated with the degree 0.7 and h5 with the degree 0.53. Since h1 has been evaluated as better than h5, A chooses the former. At this point the communication can continue as a dialogue between A and C in a similar way as above. The aim is now finding a suitable parking close to the chosen hotel h1 and then asking to navigate to the chosen parking place: OwOt [0 Messagewt 0 A 0 C OwOt [0 Seekwt [0 Suitablep wt 0 A 0 Parking]]] 11 Here we use the classical set-theoretic notation without trivialisation, for the sake of simplicity. M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 36
- 53. OwOt [0 Messagewt 0 C 0 A OwOt [0 Unrecognisedwt 00 Suitablep ] OwOt [0 Messagewt 0 A 0 C OwOt [0 Refinewt 0 [0 Suitablep wt 0 A 0 Parking] = 0 [OwOt Ox [[0 Parkingwt x] š [[0 Evaluatep wt 0 A [0 Pricewt x] [0 DistEwt x]] t 0 0.5]]]]] OwOt [0 Messagewt 0 C 0 A OwOt [0 Answerwt [0 Suitablep wt 0 A 0 Parking]] = {{p2,0.93},{p1,0.53}] The message closing the dialogue might be sent from A to C: OwOt [0 Messagewt 0 A 0 C OwOt [0 Orderwt OwOt [0 Navigate-towt 0 p2]]]. At this point the agent C must have 0 Navigate-to in his/her ontology (if he/she does not then the learning process described above begins); C thus knows that he/she has to call another agent D which is a GIS-agent that provides navigation facilities (see [6]). Concluding this paragraph we again compare the TIL approach with EL@ . An analogy to the above described means of communication can be found in the DL community. There are heuristics for the top-k search (see [13]). However, these facilities lack any formal / logic / semantic specification. The development of description logic and its variants can be considered as a step forward to the development of languages which extend W3C standards. In [9] a step in this direction is described. In particular the EL@ variant of the description logic can be embedded into classical two-valued description logic with concrete domains (see [1]), and thus also into OWL (or a slight extension of it). Using the results described in this paper, especially the added value of TIL, we can expect the extension of W3C based specification of web service languages using the OWL representation. 5. Conclusion: A hybrid system In the previous chapters, especially by using the parallel description of our motivating example in Chapter 4, we tried to show that TIL and EL@ have many features in common. Both the systems can share some basic types, functions, concepts and roles; both the systems distinguish extensional and intentional context (the former being modelled by the intensional descent in TIL and A-Boxes in DL, the latter illustrated here by the (user-) definition or specification of a multi-criterion search). These features can form the intersection TIE@L. On the other hand, both the systems can be enhanced by accommodating features of the other system, thus forming a union TI+E@L. The main contribution of EL@ is the method of modelling multi-criterion aspects of user preferences (some heuristics have been tested in separate works), and computing global user preferences by means of the aggregation functions and scaling. TIL contributes to this union the method of a very fine-grained and rigorous knowledge specification closed to natural language, including procedural hyper- intensional semantics. We are convinced that these aspects are crucial for a smooth communication and reasoning of agents in the multi-agent world. Artificial Intelligence is sometimes characterised as a ‘struggle for consistency’. To put it slightly metaphorically, reality is consistent. Only our ‘making it explicit’ in language may lead to paradoxes and inconsistencies due to misinterpretations that are caused by a too coarse-grained analysis of assumptions. The specification of the formal model of the hybrid system is however still a subject of further research. Currently we plan to perform experiments and tests on real data using the hints described in Chapter 4. M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 37
- 54. In the team led by M. Duží, working on the project “Logic and Artificial Intelligence for multi-agent systems” (see http://labis.vsb.cz/), we pursue research on multi-agent systems based on TIL. Currently we implemented software modules simulating the behaviour of mobile agents in a traffic system. The agents can choose particular realisations of their pre- defined processes; moreover, they are able to dynamically adjust their behaviour dependently on changing states of affairs in the environment. They communicate by message-exchange system. To this end the TIL-Script language (see [14]) has been designed and it is currently being implemented. We also plan to test some modules with EL@ features. The project in which P. Vojtas is involved (see [17]) deals with theoretical models compatible with W3C standards and experimental testing of multi-criterion search dependent on user preferences. We believe that the TIL features will enhance the system with a rigorous semantic description and specification of the software / implementation parts. When pursuing the research we soon came to the conclusion that the area of the semantic web and multi-agent world in general is so broad that it is almost impossible to create a universal development method. Instead we decided to develop a methodology comprising and integrating particular existing and/or newly developed methods as well as our fine-grained rigorous logic. The paper is an introductory study aiming at a more universal logical approach to the ‘multi-agent world’, which at the same time opens new research problems and trends. The main challenges are formal measures (soundness and completeness) and implementation measures of the integrated hybrid system. –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ACKNOWLEDGEMENTS This work has been supported by the project No. 1ET101940420 “Logic and Artificial Intelligence for multi- agent systems” within the program “Information Society” of the Czech Academy of Sciences, and by the “Semantic Web” project No. 1ET100300419 of the Czech IT agency. REFERENCES [1] Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. eds. (2002): Description Logic Handbook, Cambridge University Press. [2] Brandt, S. (2004): Polynomial Time Reasoning in a Description Logic with Existential Restrictions, GCI Axioms, and What Else? In R. López de Mantáras et al. eds. In Proc. ECAI-2004, pp. 298-302. IOS Press. [3] Church, A. (1956): Introduction to Mathematical Logic I. Princeton. [4] Cresswell, M.J. (1985): Structured meanings. MIT Press, Cambridge, Mass. [5] Duží, M.(2004): Concepts, Language and Ontologies (from the logical point of view). In Information Modelling and Knowledge Bases XV. Ed. Y. Kiyoki, H. Kangassalo, E Kawaguchi, IOS Press Amsterdam, Vol. XV, 193-209. [6] Duží, M., Ćuráková, D., DČrgel, P., Gajdoš, P., Müller, J. (2007): Logic Artificial Inteligence for Multi- Agent Systems. In Information Modelling and Knowledge Bases XVIII. M. Duží, H. Jaakkola, Y. Kyioki, H.Kangassalo (Eds.), IOS Press Amsterdam, 236-244. [7] Duží, M., Heimburger A. (2006): Web Ontology Languages: Theory and practice, will they ever meet?. In Information Modelling and Knowledge Bases XVII. Ed. Y. Kiyoki, J. Henno, H. Jaakkola, H. Kangassalo, IOS Press Amsterdam, Vol. XVII, 20-37. [8] Duží, M., Jespersen B, Müller, J. (2005): Epistemic Closure and Inferable Knowledge. In the Logica Yearbook 2004. Ed. Libor BČhounek, Marta Bílková, Filosofia Praha, Vol. 2004, 1-15. [9] Eckhardt, A., Pokorný, J., Vojtáš, P. (2006): Integrating user and group preferences for top-k search from distributed web resources, technical report 2006 [10] Fagin, R. (1999): Combining fuzzy information from multiple systems, Journal of Comput. System Sci. 58, 1999, 83-99 [11] Feferman, S. (1995): ‘Definedness’. Erkenntnis 43, pp. 295-320. [12] Gamut, L.T.F. (1991): Logic, Language and Meaning. Volume II. Intensional Logic and Logical Grammar. M. Duží and P. Vojtáš / Multi-Criterion Search from the Semantic Point of View 38
- 55. Other documents randomly have different content
- 56. CHAPTER III The Army of the Union: The Children and the Flag The Army of the Union entered Richmond with almost the solemnity of a processional entering church. It was occasion for solemn procession, that entrance into our burning city where a stricken people, flesh of their flesh and bone of their bone, watched in terror for their coming. Our broken-hearted people closed their windows and doors and shut out as far as they could all sights and sounds. Yet through closed lattice there came that night to those living near Military Headquarters echoes of rejoicings. Early that fateful morning, Mayor Mayo, Judge Meredith and Judge Lyons went out to meet the incoming foe and deliver up the keys of the city. Their coach of state was a dilapidated equipage, the horses being but raw-boned shadows of better days when there were corn and oats in the land. They carried a piece of wallpaper, on the unflowered side of which articles of surrender were inscribed in dignified terms setting forth that “it is proper to formally surrender the City of Richmond, hitherto Capital of the Confederate States of America.” Had the words been engraved on satin in letters of gold, Judge Lyons (who had once represented the United States at the Court of St. James) could not have performed the honours of introduction between the municipal party and the Federal officers with statelier grace, nor could the latter have received the instrument of submission with profounder courtesy. “We went out not knowing what we would encounter,” Mayor Mayo reported, “and we met a group of Chesterfields.” Major Atherton H. Stevens, of General Weitzel’s staff, was the immediate recipient of the wallpaper document.
- 57. General Weitzel and his associates were merciful to the stricken city; they aided her people in extinguishing the flames; restored order and gave protection. Guards were posted wherever needed, with instructions to repress lawlessness, and they did it. To this day, Richmond people rise up in the gates and praise that Army of the Occupation as Columbia’s people can never praise General Sherman’s. Good effect on popular sentiment was immediate. Among many similar incidents of the times is this, as related by a prominent physician: “When I returned from my rounds at Chimborazo I found a Yankee soldier sitting on my stoop with my little boy, Walter, playing with the tassels and buttons on his uniform. He arose and saluted courteously, and told me he was there to guard my property. ‘I am under orders,’ he said, ‘to comply with any wish you may express.’” Dr. Gildersleeve, in an address (June, 1904) before the Association of Medical Officers of the Army and Navy, C. S. A., referred to Chimborazo Hospital as “the most noted and largest military hospital in the annals of history, ancient or modern.” With its many white buildings and tents on Chimborazo Hill, it looked like a town and a military post, which latter it was, with Dr. James B. McCaw for Commandant. General Weitzel and his staff visited the hospital promptly. Dr. McCaw and his corps in full uniform received them. Dr. Mott, General Weitzel’s Chief Medical Director, exclaimed: “Ain’t that old Jim McCaw?” “Yes,” said “Jim McCaw,” “and don’t you want a drink?” “Invite the General, too,” answered Dr. Mott. General Weitzel issued passes to Dr. McCaw and his corps, and gave verbal orders that Chimborazo Confederates should be taken care of under all circumstances. He proposed to take Dr. McCaw and his corps into the Federal service, thus arming him with power to make requisition for supplies, medicines, etc., which offer the doctor, as a loyal Confederate, was unable to accept. Others of our physicians and surgeons found friends in Federal ranks. To how many poor Boys in Blue, longing for home and
- 58. kindred, had not they and our women ministered! The orders of the Confederate Government were that the sick and wounded of both armies should be treated alike. True, nobody had the best of fare, for we had it not to give. We were without medicines; it was almost impossible to get morphia, quinine, and other remedies. Quinine was $400 an ounce, when it could be bought at all, even in the earlier years of the war. Our women became experts in manufacturing substitutes out of native herbs and roots. We ran wofully short of dressings and bandages, and bundles of old rags became treasures priceless. But the most cruel shortage was in food. Bitter words in Northern papers and by Northern speakers—after our defeat intensified, multiplied, and illustrated—about our treatment of prisoners exasperated us. “Will they never learn,” we asked, “that on such rations as we gave our prisoners, our men were fighting in the field? We had not food for ourselves; the North blockaded us so we could not bring food from outside, and refused to exchange prisoners with us. What could we do?” I wonder how many men now living remember certain loaves of wheaten bread which the women of Richmond collected with difficulty in the last days of the war and sent to Miss Emily V. Mason, our “Florence Nightingale,” for our own boys. “Boys,” Miss Emily announced—sick soldiers, if graybeards, were “boys” to “Cap’n,” as they all called Miss Emily—“I have some flour-bread which the ladies of Richmond have sent you.” Cheers, and other expressions of thankfulness. “The poor, sick Yankees,” Miss Emily went on falteringly—uneasy countenances in the ward—“can’t eat corn-bread —” “Give the flour-bread to the poor, sick Yankees, Cap’n!” came in cheerful, if quavering chorus from the cots. “We can eat corn-bread. Gruel is good for us. We like mush. Oughtn’t to have flour-bread nohow.” “Poor fellows!” “Cap’n” said proudly of their self-denial, “they were tired to death of corn-bread in all forms, and it was not good for them, for nearly all had intestinal disorders.” Along with this corn-bread story, I recall how Dr. Minnegerode, Protestant, and Bishop Magill, Catholic, used to meet each other on
- 59. the street, and the one would say: “Doctor, lend me a dollar for a sick Yankee.” And the other: “Bishop, I was about to ask you for a dollar for a sick Yankee.” And how Annie E. Johns, of North Carolina, said she had seen Confederate soldiers take provisions from their own haversacks and give them to Federal prisoners en route to Salisbury. As matron, she served in hospitals for the sick and wounded of both armies. She said: “When I was in a hospital for Federals, I felt as if these men would defend me as promptly as our own.” In spite of the pillage, vandalism and violence they suffered, Southern women were not so biassed as to think that the gentle and brave could be found only among the wearers of the gray. Even in Sherman’s Army were the gentle and brave upon whom fell obloquy due the “bummers” only. I have heard many stories like that of the boyish guard who, tramping on his beat around a house he was detailed to protect, asked of a young mother: “Why does your baby cry so?” She lifted her pale face, saying: “My baby is hungry. I have had no food—and so—I have no nourishment for him.” Tears sprang into his eyes, and he said: “I will be relieved soon; I will draw my rations and bring them to you.” He brought her his hands full of all good things he could find—sugar, tea, and coffee. And like that of two young Philadelphians who left grateful hearts behind them along the line of Sherman’s march because they made a business of seeing how many women and children they could relieve and protect. In Columbia, during the burning, men in blue sought to stay ravages wrought by other men in blue. I hate to say hard things of men in blue, and I must say all the good things I can; because many were unworthy to wear the blue, many who were worthy have carried reproach. On that morning of the occupation, our women sat behind closed windows, unable to consider the new path stretching before them. The way seemed to end at a wall. Could they have looked over and seen what lay ahead, they would have lost what little heart of hope they had; could vision have extended far enough, they might have
- 60. won it back; they would have beheld some things unbelievable. For instance, they would have seen the little boy who played with the buttons and tassels, grown to manhood and wearing the uniform of an officer of the United States; they would have seen Southern men walking the streets of Richmond and other Southern cities with “U. S. A.” on their haversacks; and Southern men and Northern men fighting side by side in Cuba and the Philippines, and answering alike to the name, “Yankees.” On the day of the occupation, Miss Mason and Mrs. Rhett went out to meet General Weitzel and stated that Mrs. Lee was an invalid, unable to walk, and that her house, like that of General Chilton and others, was in danger of fire. “What!” he exclaimed, “Mrs. Lee in danger? General Fitz Lee’s mother, who nursed me so tenderly when I was sick at West Point! What can I do for her? Command me!” “We mean Mrs. Robert E. Lee,” they said. “We want ambulances to move Mrs. Lee and other invalids and children to places of safety.” Using his knee as a writing-table, he wrote an order for five ambulances; and the ladies rode off. Miss Emily’s driver became suddenly and mysteriously tipsy and she had to put an arm around him and back up the vehicle herself to General Chilton’s door, where his children, her nieces, were waiting, their dollies close clasped. “Come along, Virginia aristocracy!” hiccoughed the befuddled Jehu. “I won’t bite you! Come along, Virginia aristocracy!” A passing officer came to the rescue, and the party were soon safely housed in the beautiful Rutherford home. The Federals filled Libby Prison with Confederates, many of whom were paroled prisoners found in the city. Distressed women surrounded the prison, begging to know if loved ones were there; others plead to take food inside. Some called, while watching windows: “Let down your tin cup and I will put something in it.” Others cried: “Is my husband in there? O, William, answer me if you are!” “Is my son, Johnny, here?” “O, please somebody tell me if my boy is in the prison!” Miss Emily passed quietly through the crowd,
- 61. her hospital reputation securing admission to the prison; she was able to render much relief to those within, and to subdue the anxiety of those without. “Heigho, Johnny Reb! in there now where we used to be!” yelled one Yankee complacently. “Been in there myself. D—d sorry for you, Johnnies!” called up another. A serio-comic incident of the grim period reveals the small boy in an attitude different from that of him who was dandled on the Federal knee. Some tiny lads mounted guard on the steps of a house opposite Military Headquarters, and, being intensely “rebel” and having no other means of expressing defiance to invaders, made faces at the distinguished occupants of the establishment across the way. General Patrick, Provost-Marshal General, sent a courteously worded note to their father, calling his attention to these juvenile demonstrations. He explained that while he was not personally disturbed by the exhibition, members of his staff were, and that the children might get into trouble. The proper guardians of the wee insurgents, acting upon this information, their first of the battery unlimbered on their door-step, saw that the artillery was retired in good order, and peace and normal countenances reigned over the scene of the late engagements. I open a desultory diary Matoaca kept, and read: “If the United States flag were my flag—if I loved it—I would not try to make people pass under it who do not want to. I would not let them. It is natural that we should go out of our way to avoid walking under it, a banner that has brought us so much pain and woe and want—that has desolated our whole land. “Some Yankees stretched a flag on a cord from tree to tree across the way our children had to come into Richmond. The children saw it and cried out; and the driver was instructed to go another way. A Federal soldier standing near—a guard, sentinel or picket—ordered
- 62. the driver to turn back and drive under that flag. He obeyed, and the children were weeping and wailing as the carriage rolled under it.” In Raymond, Mississippi, negro troops strung a flag across the street and drove the white children under it. In Atlanta, two society belles were arrested because they made a detour rather than walk under the flag. Such desecration of the symbol of liberty and union was committed in many places by those in power. The Union flag is my flag and I love it, and, therefore, I trust that no one may ever again pass under it weeping. Those little children were not traitors. They were simply human. If in the sixties situations had been reversed, and the people of New York, Boston and Chicago had seen the Union flag flying over guns that shelled these cities, their children would have passed under it weeping and wailing. Perhaps, too, some would have sat on doorsteps and “unbeknownst” to their elders have made faces at commanding generals across the way; while others climbing upon the enemy’s knees would have played with gold tassels and brass buttons. Our newspapers, with the exception of the “Whig” and the “Sentinel,” shared in the general wreckage. A Northern gentleman brought out a tiny edition of the former in which appeared two military orders promulgating the policy General Weitzel intended to pursue. One paragraph read: “The people of Richmond are assured that we come to restore to them the blessings of peace and prosperity under the flag of the Union.” General Shepley, Military Governor by Weitzel’s appointment, repeated this in substance, adding: “The soldiers of the command will abstain from any offensive or insulting words or gestures towards the citizens.” With less tact and generosity, he proceeded: “The Armies of the Rebellion having abandoned their efforts to enslave the people of Virginia, have endeavoured to destroy by fire their Capital.... The first duty of the Army of the Union will be to save the city doomed to destruction by the Armies of the Rebellion.”
- 63. That fling at our devoted army would have served as a clarion call to us—had any been needed—to remember the absent. “It will be a blunder in us not to overlook that blunder of General Shepley’s,” urged Uncle Randolph.[1] “The important point is that the policy of conciliation is to be pursued.” With the “Whig” in his hand, Uncle Randolph told Matoaca that the Thursday before Virginia seceded a procession of prominent Virginians marched up Franklin Street, carrying the flag of the Union and singing “Columbia,” and that he was with them. The family questioned if his mind were wandering, when he went on: “The breach can be healed—in spite of the bloodshed—if only the Government will pursue the right course now. Both sides are tired of hating and being hated, killing and being killed—this war between brothers—if Weitzel’s orders reflect the mind of Lincoln and Grant—and they must—all may be well—before so very long.” These were the men of the Union Army who saved Richmond: The First Brigade, Third Division (Deven’s Division), Twenty-fourth Army Corps, Army of the James, Brevet-Brigadier-General Edward H. Ripley commanding. This brigade was composed of the Eleventh Connecticut, Thirteenth New Hampshire, Nineteenth Wisconsin, Eighty-first New York, Ninety-eighth New York, One Hundredth and Thirty-ninth New York, Convalescent detachment from the second and third divisions of Sheridan’s reinforcements. “This Brigade led the column in the formal entry, and at the City Hall halted while I reported to Major-General Weitzel,” says General Ripley. “General Weitzel had taken up his position on the platform of the high steps at the east front of the Confederate Capitol, and there, looking down into a gigantic crater of fire, suffocated and blinded with the vast volumes of smoke and cinders which rolled up over and enveloped us, he assigned me and my brigade to the apparently hopeless task of stopping the conflagration, and suppressing the mob of stragglers, released criminals, and negroes, who had far advanced in pillaging the city. He had no suggestions to
- 64. make, no orders to give, except to strain every nerve to save the city, crowded as it was with women and children, and the sick and wounded of the Army of Northern Virginia. “After requesting Major-General Weitzel to have all the other troops marched out of the city, I took the Hon. Joseph Mayo, then Mayor of Richmond, with me to the City Hall, where I established my headquarters. With the help of the city officials, I distributed my regiment quickly in different sections. The danger to the troops engaged in this terrific fire-fighting was infinitely enhanced by the vast quantities of powder and shells stored in the section burning. Into this sea of fire, with no less courage and self-devotion than as though fighting for their own firesides and families, stripped and plunged the brave men of the First Brigade. “Meanwhile, detachments scoured the city, warning every one from the streets to their houses.... Every one carrying plunder was arrested.... The ladies of Richmond thronged my headquarters, imploring protection. They were sent to their homes under the escort of guards, who were afterwards posted in the center house of each block, and made responsible for the safety of the neighborhood.... Many painful cases of destitution were brought to light by the presence of these safeguards in private houses, and the soldiers divided rations with their temporary wards, in many cases, until a general system of relief was organised.”[2] THE COMING OF LINCOLN
- 65. CHAPTER IV The Coming of Lincoln The South did not know that she had a friend in Abraham Lincoln, and the announcement of his presence in Richmond was not calculated to give comfort or assurance. “Abraham Lincoln came unheralded. No bells rang, no guns boomed in salute. He held no levee. There was no formal jubilee. He must have been heartless as Nero to have chosen that moment for a festival of triumph. He was not heartless.” So a citizen of Richmond, who was a boy at the time, and out doors and everywhere, seeing everything, remembers the coming of Lincoln. One of the women who sat behind closed windows says: “If there was any kind of rejoicing, it must have been of a very somber kind; the sounds of it did not reach me.” Another who looked through her shutters, said: “I saw him in a carriage, the horses galloping through the streets at a break-neck speed, his escort clearing the way. The negroes had to be cleared out of the way, they impeded his progress so.” He was in Richmond April 4 and 5, and visited the Davis Mansion, the Capitol, Libby Prison, Castle Thunder and other places. His coming was as simple, business-like, and unpretentious as the man himself. Anybody who happened to be in the neighbourhood on the afternoon of April 4, might have seen a boat manned by ten or twelve sailors pull ashore at a landing above Rockett’s, and a tall, lank man step forth, “leading a little boy.” By resemblance to pictures that had been scattered broadcast, this man could have been easily recognized as Abraham Lincoln. The little boy was Tad, his son. Major Penrose, who commanded the escort, says Tad was not with
- 66. the President; Admiral Porter, General Shepley and others say he was. Accompanied by Admiral Porter and several other officers and escorted by ten sailors, President Lincoln, “holding Tad’s hand,” walked through the city, which was in part a waste of ashes, and the smoke of whose burning buildings was still ascending. From remains of smouldering bridges, from wreckage of gunboats, from Manchester on the other side of the James, and from the city’s streets smoke rose as from a sacrifice to greet the President. A Northern newspaper man (who related this story of himself) recognizing that it was his business to make news as well as dispense it, saw some negroes at work near the landing where an officer was having débris removed, and other negroes idling. He said to this one and to that: “Do you know that man?” pointing to the tall, lank man who had just stepped ashore. “Who is dat man, marster?” “Call no man marster. That man set you free. That is Abraham Lincoln. Now is your time to shout. Can’t you sing, ‘God bless you, Father Abraham!’” That started the ball rolling. The news spread like wild-fire. Mercurial blacks, already excited to fever-heat, collected about Mr. Lincoln, impeding his progress, kneeling to him, hailing him as “Saviour!” and “My Jesus!” They sang, shouted, danced. One woman jumped up and down, shrieking: “I’m free! I’m free! I’m free till I’m fool!” Some went into the regular Voodoo ecstasy, leaping, whirling, stamping, until their clothes were half torn off. Mr. Lincoln made a speech, in which he said: “My poor friends, you are free—free as air. But you must try to deserve this priceless boon. Let the world see that you merit it by your good works. Don’t let your joy carry you into excesses. Obey God’s commandments and thank Him for giving you liberty, for to Him you owe all things. There, now, let me pass on. I have little
- 67. time here and much to do. I want to go to the Capitol. Let me pass on.” Henry J. Raymond speaks of the President as taking his hat off and bowing to an old negro man who knelt and kissed his hand, and adds: “That bow upset the forms, laws and customs of centuries; it was a death-shock to chivalry, a mortal wound to caste. Recognize a nigger? Faugh!” Which proves that Mr. Raymond did not know or wilfully misrepresented a people who could not make reply. Northern visitors to the South may yet see refutation in old sections where new ways have not corrupted ancient courtesy, and where whites and blacks interchange cordial and respectful salutations, though they may be perfect strangers to each other, when passing on the road. If they are not strangers, greeting is usually more than respectful and cordial; it is full of neighbourly and affectionate interest in each other and each other’s folks. The memories of the living, even of Federal officers near President Lincoln, bear varied versions of his visit. General Shepley relates that he was greatly surprised when he saw the crowd in the middle of the street, President Lincoln and little Tad leading, and that Mr. Lincoln called out: “Hullo, General! Is that you? I’m walking around looking for Military Headquarters.” General Shepley conducted him to our White House, where President Lincoln wearily sank into a chair, which happened to be that President Davis was wont to occupy while writing his letters, a task suffering frequent interruption from some one or other of his children, who had a way of stealing in upon him at any and all times to claim a caress. Upon Mr. Lincoln’s arrival, or possibly in advance, when it was understood that he would come up from City Point, there was discussion among our citizens as to how he should be received—that is, so far as our attitude toward him was concerned. There were
- 68. several ways of looking at the problem. Our armies were still in the field, and all sorts of rumors were afloat, some accrediting them with victories. A called meeting was held under the leadership of Judge Campbell and Judge Thomas, who, later, with General Joseph Anderson and others, waited on Mr. Lincoln, to whom they made peace propositions involving disbandment of our armies; withdrawal of our soldiers from the field, and reëstablishment of state governments under the Union, Virginia inaugurating this course by example and influence. Mr. Lincoln had said in proclamation, the Southern States “can have peace any time by simply laying down their arms and submitting to the authority of the Union.” It was inconceivable to many how we could ever want to be in the Union again. But wise ones said: “Our position is to be that of conquered provinces voiceless in the administration of our own affairs, or of States with some power, at least, of self-government.” Then, there was the dread spectre of confiscation, proscription, the scaffold. Judge Campbell and Judge Thomas reported: “The movement for the restoration of the Union is highly gratifying to Mr. Lincoln; he will give it full sympathy and coöperation.”
- 69. THE WHITE HOUSE OF THE CONFEDERACY, RICHMOND, VA. Presented to Mr. Davis, who refused it as a gift, but occupied it as the Executive residence. Now known as the Confederate Museum. “You people will all come back now,” Mr. Lincoln had said to Judge Thomas, “and we shall have old Virginia home again.” Many had small faith in these professions of amity, and said so. “Lincoln is the man who called out the troops and precipitated war,” was bitterly objected, “and we do not forget Hampton Roads.” A few built hopes on belief that Mr. Lincoln had long been eager to harmonize the sections. Leader of these was Judge John A. Campbell, ex-Associate Justice of the Supreme Court of the United States, and ex-Assistant Secretary of War of the expiring Confederacy. He had served with Mr. Hunter and Mr. Stephens on the
- 70. Hampton Roads Peace Commission, knew Mr. Lincoln well, had high regard for him and faith in his earnest desire for genuine reconciliation between North and South. When the Confederate Government left the city, he remained, meaning to try to make peace, Mr. Davis, it is said, knowing his purpose and consenting, but having no hope of its success. Only the Christmas before, when peace sentiments that led to the Hampton Roads Conference were in the air, striking illustrations in Northern journals reflected Northern sentiment. One big cartoon of a Christmas dinner in the Capitol at Washington, revealed Mr. Lincoln holding wide the doors, and the seceded States returning to the family love feast. Olive branches, the “Prodigal’s Return,” and nice little mottoes like “Come Home, Our Erring Sisters, Come!” were neatly displayed around the margin. Fatted calves were not to be despised by a starving people; but the less said about the pious influences of the “Prodigal’s Return” the better. That Hampton Roads Conference (February, 1865) has always been a sore spot. In spite of the commissioners’ statements that Mr. Lincoln’s only terms were “unconditional surrender,” many people blamed Mr. Davis for the failure of the peace movement; others said he was pusillanimous and a traitor for sanctioning overtures that had to be made, by Lincoln’s requirements, “informally,” and, as it were, by stealth. “We must forget dead issues,” our pacificators urged. “We have to face the present. The stand Mr. Lincoln has taken all along, that the Union is indissoluble and that a State can not get out of it however much she tries, is as fortunate for us now as it was unlucky once.” “In or out, what matters it if Yankees rule over us!” others declared. “Mr. Lincoln is not in favor of outsiders holding official reins in the South,” comforters responded. “He has committed himself on that point to Governor Hahn in Louisiana. When Judge Thomas suggested that he establish Governor Pierpont here, Mr. Lincoln asked straightway, ‘Where is Extra Billy?’ He struck the table with his fist, exclaiming, ‘By Jove! I want that old game-cock back here!’”
- 71. When in 1862-3 West Virginia seceded from Virginia and was received into the bosom of the Union, a few “loyal” counties which did not go with her, elected Francis H. Pierpont Governor of the old State. At the head of sixteen legislators, he posed at Alexandria as Virginia’s Executive, Mr. Lincoln and the Federal Congress recognizing him. Our real governor was the doughty warrior, William Smith, nick- named “Extra Billy” before the war, when he was always asking Congress for extra appropriations for an ever-lengthening stage- coach and mail-route line, which was a great Government enterprise under his fostering hand. Governor Smith had left with the Confederate Government, going towards Lynchburg. He had been greatly concerned for his family, but his wife had said: “I may feel as a woman, but I can act like a man. Attend to your public affairs and I will arrange our family matters.” The Mansion had barely escaped destruction by fire. The Smith family had vacated it to the Federals, had been invited to return and then ordered to vacate again for Federal occupation. Mr. Lincoln said that the legislature that took Virginia out of the Union and Governor Letcher, who had been in office then, with Governor Smith, his successor, and Governor Smith’s legislature, must be convened. “The Government that took Virginia out of the Union is the Government to bring her back. No other can effect it. They must come to the Capitol yonder where they voted her out and vote her back.” Uncle Randolph was one of those who had formally called upon Mr. Lincoln at the Davis Mansion. Feeble as he was, he was so eager to do some good that he had gone out in spite of his niece to talk about the “policy” he thought would be best. “I did not say much,” he reported wistfully. “There were a great many people waiting on him. Things look strange at the Capitol. Federal soldiers all about, and campfires on the Square. Judge Campbell introduced me. President Lincoln turned from him to me, and said: ‘You fought for the Union in Mexico.’ I said, ‘Mr. Lincoln, if the Union will be fair to Virginia, I will fight for the Union again.’ I forgot, you see, that I am
- 72. too old and feeble to fight. Then I said quickly, ‘Younger men than I, Mr. President, will give you that pledge.’ What did he say? He looked at me hard—and shook my hand—and there wasn’t any need for him to say anything.” Mr. Lincoln’s attitude towards Judge Campbell was one of confidence and cordiality. He knew the Judge’s purity and singleness of purpose in seeking leniency for the conquered South, and genuine reunion between the sections. The Federal commanders understood his devotion and integrity. The newspaper men, in their reports, paid respect to his venerable, dignified figure, stamped with feebleness, poverty, and a noble sorrow, waiting patiently in one of the rooms at the Davis Mansion for audience with Mr. Lincoln. None who saw Mr. Lincoln during that visit to Richmond observed in him any trace of exultation. Walking the streets with the negroes crowding about him, in the Davis Mansion with the Federal officers paying him court and our citizens calling on him, in the carriage with General Weitzel or General Shepley, a motley horde following—he was the same, only, as those who watched him declared, paler and wearier-looking each time they saw him. Uncle Randolph reported: “There was something like misgiving in his eyes as he sat in the carriage with Shepley, gazing upon smoking ruins on all sides, and a rabble of crazy negroes hailing him as ‘Saviour!’ Truly, I never saw a sadder or wearier face in all my life than Lincoln’s!” He had terrible problems ahead, and he knew it. His emancipation proclamation in 1863 was a war measure. His letter to Greeley in 1862, said: “If there be those who would not save the Union unless they could at the same time save slavery, I do not agree with them. If I could preserve the Union without freeing any slaves, I would do it; if I could preserve the Union by freeing all the slaves, I would do it.... What I do about the coloured race, I do because I think it helps to save the Union.”
- 73. GOVERNOR’S MANSION, RICHMOND, VA. Erected 1811-13, to succeed a plain wooden structure called the “Governor’s Palace.” To a committee of negroes waiting on him in the White House, August 14, 1862, Mr. Lincoln named colonisation as the one remedy for the race trouble, proposing Government aid out of an appropriation which Congress had voted him. He said: “White men in this country are cutting each other’s throats about you. But for your race among us, there would be no war, although many men on either side do not care for you one way or the other.... Your race suffers from living among us, ours from your presence.” He applied $25,000 to the venture, but it failed; New Grenada objected to negro colonisation. Two months before his visit to Richmond, some official (Colonel Kaye, as I remember) was describing to him the extravagancies of South Carolina negroes when Sherman’s army announced freedom
- 74. to them, and Mr. Lincoln walked his floor, pale and distressed, saying: “It is a momentous thing—this liberation of the negro race.” He left a paper in his own handwriting with Judge Campbell, setting forth the terms upon which any seceded State could be restored to the Union; these were, unqualified submission, withdrawal of soldiers from the field, and acceptance of his position on the slavery question, as defined in his proclamations. The movement gained ground. A committee in Petersburg, headed by Anthony Keiley, asked permits to come to Richmond that they might coöperate with the committee there. “Unconditional surrender,” some commented. “Mr. Lincoln is not disposed to humiliate us unnecessarily,” was the reassurance. “He promised Judge Campbell that irritating exactions and oaths against their consciences are not to be imposed upon our people; they are to be encouraged, not coerced, into taking vows of allegiance to the United States Government; Lincoln’s idea is to make allegiance a coveted privilege; there are to be no confiscations; amnesty to include our officers, civil and military, is to be granted—that is, the power of pardon resting with the President, he pledges himself to liberal use of it. Lincoln is long-headed and kind-hearted. He knows the best thing all around is a real peace. He wishes to restore confidence in and affection for the Union. That is plain. He said: ‘I would gladly pardon Jeff Davis himself if he would ask it.’” I have heard one very pretty story about Mr. Lincoln’s visit to Richmond. General Pickett, of the famous charge at Gettysburg, had been well known in early life to Mr. Lincoln when Mr. Lincoln and Mr. Johnson, General Pickett’s uncle, were law partners in Illinois. Mr. Lincoln had taken warm interest in young George Pickett as a cadet at West Point, and had written him kindly, jovial letters of advice. During that hurried sojourn in Richmond, Abraham Lincoln took time for looking up Mr. Johnson. His carriage and armed retinue drew up in front of the old Pickett mansion. The General’s beautiful young wife, trembling with alarm, heard a strange voice asking first for Mr. Johnson and then about General Pickett, and finally: “Is General
- 75. Pickett’s wife here?” She came forward, her baby in her arms. “I am General Pickett’s wife.” “Madam, I am George’s old friend, Abraham Lincoln.” “The President of the United States!” “No,” with a kindly, half-quizzical smile, “only Abraham Lincoln, George’s old friend. And this is George’s baby?” Abraham Lincoln bent his kindly, half-sad, half-smiling glance upon the child. Baby George stretched out his hands; Lincoln took him, and the little one, in the pretty fashion babies have, opened his mouth and kissed the President. “Tell your father,” said Lincoln, “that I will grant him a special amnesty—if he wants it—for the sake of your mother’s bright eyes and your good manners.” A short while after that—when Lincoln was dead—that mother was flying, terror-stricken, with her baby to Canada, where General Pickett, in fear of his life, had taken refuge. Mr. Lincoln left instructions for General Weitzel to issue passes to the legislators and State officials who were to come to Richmond for the purpose of restoring Virginia to the Union. The “Whig” had sympathetic articles on “Reconstruction,” and announced in due order the meeting of citizens called “to consider President Lincoln’s proposition for reassembling the Legislature to take Virginia back into the Union.” It printed the formal call for reassembling, signed by the committee and many citizens, and countersigned by General Weitzel; handbills so signed were printed for distribution. General Shepley, whose cordial acquiescence in the conciliation plan had been pronounced, said in after years that he suffered serious misgivings. When General Weitzel directed him to issue the passes for the returning legislators, he inquired: “Have you the President’s written order for this?” “No. Why?” “For your own security you should have it, General. When the President reaches Washington and the Cabinet are informed of what has been done and what is contemplated, this order will be rescinded, and the Cabinet will deny that it has ever been issued.” “I have the President’s commands. I am a soldier and obey orders.”
- 76. “Right, General. Command me and I obey.” Mr. Lincoln’s written order reiterating oral instructions came, however. Admiral Porter, according to his own account, took President Lincoln to task for his concessions, and told him in so many words that he was acting outside of his rights; Richmond, being under military rule, was subject to General Grant’s jurisdiction. The Admiral has claimed the distinction of working a change in the President’s mind and of recovering immediately the obnoxious order from Weitzel, killing, or trying to kill, a horse or so in the undertaking. He characterised the efforts of Judges Campbell and Thomas to serve their country and avert more bloodshed as “a clever dodge to soothe the wounded feelings of the people of the South.” The Admiral adds: “But what a howl it would have raised in the North!” Admiral Porter says the lectured President exclaimed: “Well, I came near knocking all the fat in the fire, didn’t I? Let us go. I seem to be putting my foot into it here all the time. Bless my soul! how Seward would have preached if he had heard me give Campbell permission to call the Legislature! Seward is an encyclopedia of international law, and laughs at my horse sense on which I pride myself. Admiral, if I were you, I would not repeat that joke yet awhile. People might laugh at you for knowing so much more than the President.” He was acting, he said, in conjunction with military authorities. General Weitzel was acting under General Grant’s instructions. The conciliatory plan was being followed in Petersburg, where General Grant himself had led the formal entry. “General Weitzel warmly approves the plan.” “He and Campbell are personal friends,” the Admiral remarked significantly. Whatever became of those horses driven out by Admiral Porter’s instructions to be killed, if need be, in the effort to recover that
- 77. order, is a conundrum. According to Admiral Porter the order had been written and given to General Weitzel while Mr. Lincoln was in the city. According to Judge Campbell and General Shepley, and the original now on file in Washington, it was written from City Point. Dated, “Headquarters Department of Virginia, Richmond, April 13, 1865,” this appeared in the “Whig” on the last afternoon of Mr. Lincoln’s life: “Permission for the reassembling of the gentlemen recently acting as the Legislature is rescinded. Should any of the gentlemen come to the city under the notice of reassembling already published, they will be furnished passports to return to their homes. Any of the persons named in the call signed by J. A. Campbell and others, who are found in the city twelve hours after the publication of this notice will be subject to arrest, unless they are residents. (Signed) E. O. C. Ord, General Commanding the Department.” General Weitzel was removed. Upon him was thrown the blame of the President’s “blunder.” He was charged with the crime of pity and sympathy for “rebels” and “traitors.” When Lincoln was dead, a high official in Washington said: “No man more than Mr. Lincoln condemned the course General Weitzel and his officers pursued in Richmond.” In more ways than one General Weitzel had done that which was not pleasing in the sight of Mr. Stanton. Assistant Secretary of War Dana had let Stanton know post-haste that General Weitzel was distributing “victuals” to “rebels.” Stanton wired to know of General Weitzel if he was “acting under authority in giving food supplies to the people of Richmond, and if so, whose?” General Weitzel answered, “Major-General Ord’s orders approved by General Grant.” Mr. Dana wrote Mr. Stanton, “Weitzel is to pay for rations by selling captured property.” General Weitzel apologised for magnanimity by explaining that the instructions of General Ord, his superior, were “to sell all the tobacco I find here and feed those in distress. A great
- 78. many persons, black and white, are on the point of starvation, and I have relieved the most pressing wants by the issue of a few abandoned rebel stores and some damaged stores of my own.” “All receivers of rations must take the oath,” Mr. Stanton wrote back. In Northern magazines left by Federal soldiers visiting negroes in Matoaca’s yard, black Cato saw caricatures of Southern ladies mixing in with negroes and white roughs and toughs, begging food at Yankee bureaus. “Miss Mato’ca,” he plead earnestly, “don’ go whar dem folks is no mo’. It will disgrace de fam’ly.” She had put pride and conscience in her pocket, drawn rations and brought home her pork and codfish. Revocation of permission for the reassembling of the Virginia Legislature was one of Mr. Lincoln’s last, if not his last, act in the War Department. Stanton gave him no peace till it was written; he handed the paper to Mr. Stanton, saying: “There! I think that will suit you!” “No,” said the Iron Chancellor of the Union. “It is not strong enough. It merely revokes your permission for the assembling of the rebel legislators. Some of these men will come to Richmond— are doubtless there now—in response to the call. You should prohibit the meeting.” Which was done. Hence, the prohibitory order in the “Whig.” Mr. Lincoln wrote, April 14, to General Van Alen, of New York: “Thank you for the assurance you give me that I shall be supported by conservative men like yourself in the efforts I may use to restore the Union, so as to make it, to use your own language, a Union of hearts as well as of hands.” General Van Alen had warned him against exposing himself in the South as he had done by visiting Richmond; and for this Mr. Lincoln thanked him briefly without admitting that there had been any peril. Laconically, he had thanked Stanton for concern expressed in a dispatch warning him to be careful about visiting Petersburg, adding, “I have already been there.”
- 79. When serenaded the Tuesday before his death, he said, in speaking of the bringing of the Southern States into practical relations with the Union: “I believe it is not only possible, but easier to do this, without deciding, or even considering, whether these States have ever been out of the Union. Finding themselves safely at home, it would be utterly immaterial whether they had ever been abroad.” His last joke—the story-tellers say it was his last—was about “Dixie.” General Lee’s surrender had been announced; Washington was ablaze with excitement. Delirious multitudes surged to the White House, calling the President out for a speech. It was a moment for easy betrayal into words that might widen the breach between sections. He said in his quaint way that he had no speech ready, and concluded humorously: “I have always thought ‘Dixie’ one of the best tunes I ever heard. I insisted yesterday that we had fairly captured it. I presented the question to the Attorney-General and he gave his opinion that it is our lawful prize. I ask the band to give us a good turn upon it.” In that little speech, he claimed of the South by right of conquest a song—and nothing more. THE LAST CAPITAL
- 80. CHAPTER V The Last Capital of the Confederacy From Richmond, Mr. Davis went to Danville. Major Sutherlin, the Commandant, met him at the station and carried him and members of his Cabinet to the Sutherlin Mansion, which then became practically the Southern Capitol. The President was busy night and day, examining and improving defenses and fortifications and planning the junction of Lee’s and Johnston’s forces. Men were seeking his presence at all hours; couriers coming and going; telegrams flying hither and thither. “In the midst of turmoil, and with such fearful cares and responsibilities upon him, he did not forget to be thoughtful and considerate of others,” I have heard Mrs. Sutherlin say. “He was concerned for me. ‘I cannot have you troubled with so many interruptions,’ he said. ‘We must seek other quarters.’ But I would not have it so. ‘All that you call a burden is my privilege,’ I replied. ‘I will not let you go.’ He had other quarters secured for the Departments, but he and members of his Cabinet remained my guests.” In that hospitable home the table was set all the time for the coming and the going. The board was spread with the best the bountiful host and hostess could supply. Mrs. Sutherlin brought out all her treasured reserves of pickles, sweetmeats and preserves. This might be her last opportunity for serving the Confederacy and its Chieftain. The Sutherlins knew that the President’s residence in their home was a perilous honour. In case the Confederacy failed—and hope to the contrary could not run high—their dwelling would be a marked spot.
- 81. Major Sutherlin had been a strong Union man. Mrs. Sutherlin has told me how her husband voted against secession in the first convention to which he was a delegate, and for it in the second, with deep regret. “I saw in that convention,” he told his wife, “strong, reserved men, men of years and dignity, sign the Secession Ordinance while tears coursed down their cheeks.” It is just to rehearse such things of men who were called “traitors” and “rebels.” It is just to remember how Jefferson Davis tried to prevent secession. His letters to New England societies, his speeches in New England and in Congress, testified to his deep and fervent desire for the “preservation of the bond between the States,” the “love of the Union in our hearts,” and “the landmarks of our fathers.” But he believed in States’ Rights as fervently as in Union of States; he believed absorption of State sovereignty into central sovereignty a violation of the Constitution. Long before secession (1847) he declined appointment of Brigadier General of Mississippi Volunteers from President Polk on the ground that the central government was not vested by the Constitution with power to commission officers of State Militia, the State having this authority.[3] Americans should not forget that this man entered the service of the Union when a lad; that his father and uncles fought in the Revolution, his brothers in the War of 1812. West Point holds trophies of his skill as a commander and of his superb gallantry on the fields of Mexico. That splendid charge without bayonets through the streets of Monterey almost to the Plaza, and the charge at Buena Vista, are themes to make American blood tingle! Their leader was not a man to believe in defeat as long as a ray of hope was left.
- 82. ST. PAUL’S CHURCH, RICHMOND, VA. It was to this church that the message was brought from Lee to Davis announcing the necessity of evacuating Richmond. As Secretary of War of the United States, Mr. Davis strengthened the power that crushed the South; in every branch of the War Department, his genius and faithful and untiring service wrought improvements. In the days of giants like Webster, Clay and Calhoun, the brilliant Mississippian drew upon himself many eyes and his course had been watched as that of a bright particular star of great promise. The candidacy of Vice-President of the United States had been tendered him—he had been mentioned for the Presidency, and
- 83. it is no wild speculation that had he abjured his convictions on the States’ Rights’ issue, he would have found himself some day in the seat Lincoln occupied. He has been accused of overweening ambition. The charge is not well sustained. He did not desire the Presidency of the Confederacy. In 1861, “Harper’s Weekly” said: “Personally, Senator Davis is the Bayard of Congress, sans peur et sans reproche; a high-minded gentleman; a devoted father; a true friend ... emphatically one of those born to command, and is doubtless destined to occupy a high position either in the Southern Confederacy or in the United States.” He was “gloriously linked with the United States service in the field, the forum, and the Cabinet.” The Southern Confederacy failed, and he was “Davis, the Arch-Traitor.” “He wrote his last proclamation on this table,” said Mrs. Sutherlin to me, her hand on the Egyptian marble where the President’s fingers had traversed that final paper of state which expressed a confidence he could not have felt, but that he must have believed it duty to affirm. He had tried to make peace and had failed. Our armies were still in the field. A bold front on his part, if it could do no more, might enable our generals to secure better terms than unconditional surrender. At least, no worse could be tendered. That final message was the utterance of a brave soul, itself disheartened, trying to put heart into others. All along the way to Danville, people had flocked to the railroad to hear him, and he had spoken as he wrote. He was an ill man, unutterably weary. He had borne the burden and heat of the day for four terrible years; he had been a target for the criticism even of his own people; all failures were laid at the door of this one man who was trying to run a government and conduct a war on an empty treasury. It must have cost him something to keep up an unwavering front. Lieutenant Wise, son of General Henry A. Wise, brought news that Lee’s surrender was imminent; on learning of it, he had taken to horse and run through the enemy’s cavalry, to warn the President.
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