![Formal Specification of DEMO Process Model
and Its Submodel
Towards Algebra of DEMO Models
Tetsuya Suga(B)
and Junichi Iijima
Tokyo Institute of Technology, 2-12-1 Ookayama,
Meguro-ku, Tokyo 152-8550, Japan
{suga.t.ac,iijima.j.aa}@m.titech.ac.jp
Abstract. This paper discusses a specification and merge operation over
submodels of a given Process Model (PM) in Design and Engineering
Methodology for Organizations (DEMO). In general, a submodel is a
part of a given model. An earlier work proposed how submodels of a given
DEMO Construction Model (CM) can be attained by a set-theoretic for-
malization. However, it remains unclear how to expand the formalism
to the notion of submodels of a given PM. Since the given PM should
align with the corresponding CM, a submodel of the given PM should
not only be a PM, but also conform to the corresponding submodel of
the CM. These two independent constraints indicate the desired defini-
tion and formalization of submodels of PMs. The proposed approach is
shown to be applicable to a common demonstration case. Through the
formalization, this paper shows the closure, commutativity, and associa-
tivity of the merge operation over submodels of a given PM. Moreover, it
is found that the consistency between CMs and PMs is preserved during
the merge operation.
Keywords: Enterprise ontology · Merge · Algebra · DEMO process
model · Match
1 Introduction
In recent years, organizations have been objects of interest in a variety of disci-
plines, not only in social science and business administration, but also in engi-
neering. Enterprise engineering (EE) is an emerging discipline of systems engi-
neering that studies organizations from an engineering perspective [1]. Since
Enterprise Ontology provides models of enterprises with considerably reduced
complexity [2], a (re)design process with such a methodology inevitably requires
working with a model of the organization rather than the real-world organization
itself. Put another way, (re)designing an enterprise is substantially achieved by
building and editing models of the enterprise, and implementing the changes in
the model in the real world.
c
Springer International Publishing AG 2017
D. Aveiro et al. (Eds.): EEWC 2017, LNBIP 284, pp. 3–17, 2017.
DOI: 10.1007/978-3-319-57955-9 1](https://image.slidesharecdn.com/19693-250610201257-b0a80646/85/Advances-in-Enterprise-Engineering-XI-7th-Enterprise-Engineering-Working-Conference-EEWC-2017-Antwerp-Belgium-May-8-12-2017-Proceedings-1st-Edition-David-Aveiro-17-320.jpg)
![4 T. Suga and J. Iijima
A vast majority of the work in this area has focused on artifacts in the
category of Way of Thinking (WoT), Way of Modeling (WoM), and Way of
Working (WoW) in five ways in information system methodologies [3], such as
artifacts that are typically involved in the process of modeling. There is, however,
relatively limited research investigating theories that may support the process of
manipulating models, a possible contribution to Way of Supporting (WoS). In
particular, the requirements of submodels of enterprise models and operations
over the submodels remain unclear.
In this article, a submodel is a part of a given model that has been already
created. The given model is often called the global model. Submodels are used
for diverse reasons and purposes, such as to partition the enterprise, to focus on
only some part in question, to hide some part for readability or even because of
an access control policy, and so on. Logically speaking, regardless of the reasons,
the requirements of those partial models of enterprise models should be specified
if we rigidly define what “part of” means. Unless they are defined properly, we
might allow submodels that do not conform to preconditions of the global model,
including (but not limited to) its metamodel. An operation over one or more
models (i.e., inputs) means creating another model by input model(s). Once the
requirements of submodels have been established, we may leverage those sub-
models by considering operations over the submodels such as merge submodels.
Such operations may include merge, diff, split, slice, and so forth. Again, if we do
not define the operation rigorously, we might get a model that does not conform
to the requirements of the global model as a result of performing the operation.
In addition, we should study and then be aware of properties of the operation
such as the associative and the commutative properties.
Insufficient investigation of the formalization and manipulability of enterprise
models, i.e., a scarcity in WoS, stands in the way of the success of EE in the
market. Presently, such a model manipulation and the following model checking
require manual work by professionals with considerable expertise not only in
the business, per se, but also in the modeling framework and theories behind
it. However a certain part of the work could be taken over or even rendered
unnecessary by formalization and automation with computer-aided design tools.
Other disciplines, such as mechanical engineering, electrical engineering, and
computer science, demonstrate the successful implementation of computer-aided
design tools and automation.
Therefore, this research aims at investigating the structure and properties in
submodels and operations in DEMO PMs based on an earlier work on those in
DEMO CMs. Although the earlier work established the formalization of CMs,
PMs are characterized by components that are specific to PMs, such as process
step kinds and causal/waiting links. Another requirement for the formalization
of PMs is to capture the relationship between a CM and a PM when they are
integrated in one DEMO model. In this article, we say that a Process Structure
Diagram (PSD, a representation of a PM) is matched to an Organization Con-
struction Diagram (OCD, a representation of CMs) as defined formally later in
Definition 13.](https://image.slidesharecdn.com/19693-250610201257-b0a80646/85/Advances-in-Enterprise-Engineering-XI-7th-Enterprise-Engineering-Working-Conference-EEWC-2017-Antwerp-Belgium-May-8-12-2017-Proceedings-1st-Edition-David-Aveiro-18-320.jpg)
![Formal Specification of DEMO Process Model and Its Submodel 5
We first propose an algebraic structure of a PSD and its submodels. In this
step, we use the set-theoretic formalization and encode the structure of a DEMO
PSD. It is because, as the earlier work [4] extensively discussed, other forms of
formalism such as Z notation, temporal logic, description logics, and category
theory turn out to be inappropriate for the purpose of the study. Those existing
formalisms not only have different structures in modularity than DEMO PSDs,
but are also inadequate for algebraic construction. In addition, it is beneficial
to use the same type of formalism with the earlier work on CMs to leverage the
knowledge and findings there. Although a PM specifies the state and transition
space of the coordination world, it seems enough to rely on the set-theoretic
formalism as long as we follow the metamodel. Secondly, an operation over the
structure, the “merge” operation, is defined and associated properties are exam-
ined by formal proofs. Then, we consider a pair-wise merge operation for OCDs
and PSDs. The result corroborates the coherence and consistency of DEMO mod-
els from a different angle. Towards the ultimate goal of constructing the algebra
of DEMO models, including four aspect models, the current research project has
worked on the algebra of PSDs. This article reports preliminary findings of the
ongoing research, which captures a DEMO PSD as a static object.
The remainder of this paper is composed as follows. In the next chapter, we
provide an overview of the background concepts and previous works related to
the issue addressed in this article. The main result is given for the construction
of an algebraic structure for DEMO PMs and an algebra over the structure, in
Sects. 3 and 4, respectively. Section 5 discusses the contribution and limitations
of this work, and concludes with a look at future directions.
2 Literature Review
2.1 Background Concepts
DEMO. Design Engineering Methodology for Organizations (DEMO) is a
modeling methodology for enterprises [2]. Although an enterprise—as an abstract
term referring to (an assembly of) collaborative activities by human beings—
has two perspectives (i.e., function and construction) in terms of systems engi-
neering, DEMO spotlights the construction perspective. In addition to its focus
on the construction of enterprises, DEMO also emphasizes the communications
within enterprises, namely from the language/action perspective. For detailed
information about DEMO, we refer the reader to [1,2].
DEMO is more suitable for the purpose and procedures of this research than
other enterprise modeling languages, including business process modeling lan-
guages. It is because it provides a strong connection between the syntax and
semantics. As shown in the rest of this article, elements of DEMO models are
formalized by mathematics and studied from their isomorphic mathematical rep-
resentations rather than the DEMO models themselves. Therefore, the strong
connection is beneficial and essential to ensure the alignment between meanings
(semantics) and symbols (syntax) when we encode DEMO models to mathemat-
ical representations and decode them back.](https://image.slidesharecdn.com/19693-250610201257-b0a80646/85/Advances-in-Enterprise-Engineering-XI-7th-Enterprise-Engineering-Working-Conference-EEWC-2017-Antwerp-Belgium-May-8-12-2017-Proceedings-1st-Edition-David-Aveiro-19-320.jpg)
![Formal Specification of DEMO Process Model and Its Submodel 7
Algebra of Structures. Now we rise to a meta-level and introduce an algebra of
(over) a structure. In the case of a set as a simple structure, the algebra of sets
defines the laws over sets, the relations over sets (e.g., equality and inclusion),
and set-theoretic operations over sets (e.g., union, intersection, and complement).
Similarly, one may construct an algebra of an arbitrary structure. The ultimate
goal of this research is to construct an algebra of DEMO models.
2.2 Related Works
Except for an earlier work [4], there exist very few formalizations for DEMO
models, namely the CRISP model [6], Petri Nets [7,8], and XML schema [9].
Though we do not repeat the details of evaluations and insufficiency of those
formalizations as a solution for the issue targeted by this research, the main
deficiencies of the existing approaches are that none of them provide algebraic
operations to form any type of algebra [4]. Since, this present work is dependent
on the formalization of DEMO OCDs in the earlier work, we recall the essen-
tial definitions and theorem here. The full descriptions, including proofs and
rationale, are available in [4].
Algebraic Structure of DEMO OCD. An algebraic structure of a DEMO
OCD is defined by elements of sets and associated operations over the sets.
Definition 1 (Society). A society S = A, T, as a universe, is made up of a
set of actor roles A and a set of transaction kinds T.
Definition 2 (Actor Role). An actor role has the following mappings:
1. fARno : A → N0
represents the number of each actor role, and
2. fARname : A → string represents the name of each actor role.
Definition 3 (Transaction Kind). A transaction kind t is a pair of actor
roles (a, a
), where a and a
are called an initiator and an executor, respectively1
.
Formally, t ∈ A × A. Transaction kinds have the following mappings:
1. fT no : T → N+
represents the number of each transaction kind,
2. fT name : T → string represents the name of each transaction kind,
3. fT in : T → A represents the initiator of each transaction kind,
4. fT ex : T → A represents the executor of each transaction kind.
Definition 4 (OCD). Given that A is a subset of A, and T is a subset of T,
an OCD is a pair A, T ∈ 2A
× 2T
that satisfies the following conditions:
Condition 1 (Unique Actor Role Name).
∀ai, ∀aj ∈ A, (fARname (ai) = fARname (aj) ⇒ ai = aj)
Condition 2 (Unique Transaction Kind Name).
∀ti, ∀tj ∈ T, (fT name (ti) = fT name (tj) ⇒ ti = tj)
1
[4] assumes that there is only one initiator for each transaction kind.](https://image.slidesharecdn.com/19693-250610201257-b0a80646/85/Advances-in-Enterprise-Engineering-XI-7th-Enterprise-Engineering-Working-Conference-EEWC-2017-Antwerp-Belgium-May-8-12-2017-Proceedings-1st-Edition-David-Aveiro-21-320.jpg)
![8 T. Suga and J. Iijima
Condition 3 (Numbering Convention).
∀t ∈ T, fARno (fT ex (t)) = fT no (t)
Condition 4 (Closure for Actor Role).
∀t ∈ T, ∀a ∈ ActorRole, a ∈ fT in (t) ∪ fT ex (t) ⇒ a ∈ A
Condition 5 (Actor Role Participation).
∀a ∈ A, ∃t ∈ T, a ∈ fT in (t) ∪ fT ex (t)
Based on this algebraic structure, we define the notion of “submodel” of a given
OCD with the following formal specification.
Definition 5 (Sub-OCD). Given an OCD A◦
, T◦
, a couple A, T is said
to be “a sub-OCD of A◦
, T◦
” if A, T is an OCD (i.e., satisfies Definition 4),
and A ⊆ A◦
and T ⊆ T◦
hold.
Algebra of DEMO OCDs. Toward the algebra of DEMO OCDs, the previous
work [4] introduced an operation over sub-OCDs of a given global OCD which
performs the merger of the two sub-OCDs. Here we repeat the definition and its
behavior as formulated in the form of theorems.
Definition 6 (OCD Merge). Given an OCD A◦
, T◦
and its two sub-OCDs
AX, TX and AY , TY , the merge operation ∇ :
2A
× 2T
×
2A
× 2T
→
2A
× 2T
is defined as AX, TX ∇ AY , TY AX ∪ AY , TX ∪ TY .
Theorem 1. The family of sub-OCDs of a given OCD is closed under the merge
operation ∇.
Theorem 2. The merge operation ∇ is commutative and associative in the fam-
ily of sub-OCDs of a given OCD.
Relationship Between a CM and a PM. Although the specification of
DEMO [5] specifies the metamodels for each aspect model separately, with less
attention to the relationship between them, there are a few articles that address
the relationship to ensure the integrity of the four aspect models. Particularly,
we use [9] as a reference, which elaborates the requirements for transformation
from a CM to a PM with coherence and consistency as “transformation rules”.
3 Construction of Algebraic Structure
This section provides a formalization of the DEMO PSD and its submodels,
which serves as the rigorous foundation for this research.
We use a common case study of Pizzeria [2] as a running example throughout
this paper. For convenience, the PSD of Pizzeria is repeated in Fig. 2. Although
it is a convention to draw actor roles with swim lanes, we omit them because
they are not included in the metamodel of the PM.](https://image.slidesharecdn.com/19693-250610201257-b0a80646/85/Advances-in-Enterprise-Engineering-XI-7th-Enterprise-Engineering-Working-Conference-EEWC-2017-Antwerp-Belgium-May-8-12-2017-Proceedings-1st-Edition-David-Aveiro-22-320.jpg)
![Formal Specification of DEMO Process Model and Its Submodel 9
3.1 PSD and Its Submodels
Algebraic Structure of PSD. As noted by the metamodel of the DEMO PM
in Fig. 1b, the PSD has transaction kinds (TK), process step kinds (PSK), and
transaction process step kinds (TPSK) as its components, with causal links and
conditional links (denoted as “TK is an initiated from TPSK” and “TPSK is a
wait condition for [another] TPSK”, respectively). As a natural and straightfor-
ward approach, these components and links are formalized as sets and relations,
respectively, below.
Let T be a set of transaction kinds. Transaction kinds have mappings to
provide the name and number, namely fT name : T → string and fT no : T → N.
This definition is to give a universe, which contains all the entities we may wish
to consider in a given situation. Thus, this set is not restricted to transaction
kinds in a particular enterprise under consideration.
I is a set of process step kinds, which consists of Production-acts and
Coordination-acts, namely I = {rq, pm, ex, st, ac} in the case of the basic trans-
action pattern2
. Since the static structure is of interest in the formalization, it
is enough for I to be a set within the scope of this article. If the dynamic aspect
in timing is considered, I should be accompanied by an order relation.
Based on the notations introduced so far, (t, i) ∈ T × I denotes a transac-
tion process step kind, as specified in the metamodel by an aggregation of a
transaction kind and a process step kind.
Example 1. Suppose we decide to consider Pizzeria as a given DEMO model. As
it is a convention that sets and relations for the given global model are indicated
by a circle ◦ in the superscript, the OCD of Pizzeria is denoted as A◦
, T ◦
,
and the PSD is denoted as T◦
, V ◦
, W◦
. In the scope of Pizzeria, we identify
four transaction kinds: T1, T2, T3, and T4. We use t with the corresponding
index to refer to these transactions kinds. Thus, the set of transaction kinds is
T = {. . . , t1, t2, t3, t4, . . .}. As clarified in Sect. 3.1, “. . .” is intentionally placed
to express that T is a universe, and hence may include other transaction kinds.
Fig. 2. PSD of Pizzeria
2
When the formalization is expanded to the standard transaction pattern, I equals
{rq, pm, ex, st, ac, dc, qt, rj, sp}.](https://image.slidesharecdn.com/19693-250610201257-b0a80646/85/Advances-in-Enterprise-Engineering-XI-7th-Enterprise-Engineering-Working-Conference-EEWC-2017-Antwerp-Belgium-May-8-12-2017-Proceedings-1st-Edition-David-Aveiro-23-320.jpg)
![12 T. Suga and J. Iijima
Fig. 3. Example in Pizzeria
3.2 Match Between a CM and a PM
Independent of Sect. 3.1, this section describes another angle to restrict the free-
dom in a formalized PSD in terms of its coherence and consistency to the corre-
sponding CM. Based on previous work [9, Chaps. 4 and 7], the requirements are
shaped as (1) the set of transaction kinds in the PSD equals that in the OCD
(up to name equivalence), and (2) the causal links between transaction kinds in
the PSD should reflect the product structure of the OCD. These are formally
defined as follows:
Definition 13 (Match). Given an OCD A, T , a PSD T, V, W is said to be
matched to the OCD if
1. T = T, and
2. ∀t, t
∈ T , (∃a ∈ A, fex (t) = a = fin (t
)) ⇐⇒ (∃i ∈ I, ((t, i) , t
) ∈ V ).
In this case, we may say an OCD and a PSD are matched.
The second condition above states the PSD is aligned to the product structure
of the enterprise. Notably, based on our formalism, the product structure is
uniquely derived from the OCD. Precisely speaking, the OCD can be uniquely
transformed to the tree of organizational building blocks, and then uniquely
converted to the tree of the product structure. According to the composition
axiom [2], a root node is uniquely identified by a transaction kind that is initiated
by the environmental actor role, or initiated by its executor itself (i.e., a self-
activated transaction kind). In a simple case such as Pizzeria, the product struc-
ture is said to be a tree, which has one root transaction. The product structures
of more complex cases, including Library [2], must be a collection of trees with
sharing. The directed adjacency relation between transaction kinds, written as
R ⊆ T × T , is uniquely obtained as R = {(t, t
) | ∃a ∈ A, fex (t) = a = fin (t
)}.
4 Algebra of PSDs
This section introduces an operation and explores its properties. As the first
step, we define the “merge” operation for two sub-PSDs of a given PSD. Then,](https://image.slidesharecdn.com/19693-250610201257-b0a80646/85/Advances-in-Enterprise-Engineering-XI-7th-Enterprise-Engineering-Working-Conference-EEWC-2017-Antwerp-Belgium-May-8-12-2017-Proceedings-1st-Edition-David-Aveiro-26-320.jpg)
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- 7. David Aveiro • Robert Pergl Giancarlo Guizzardi • João Paulo Almeida Rodrigo Magalhães • Hans Lekkerkerk (Eds.) Advances in Enterprise Engineering XI 7th Enterprise Engineering Working Conference, EEWC 2017 Antwerp, Belgium, May 8–12, 2017 Proceedings 123
- 8. Editors David Aveiro University of Madeira and Madeira Interactive Technologies Institute Funchal Portugal Robert Pergl Czech Technical University in Prague Prague Czech Republic Giancarlo Guizzardi Free University of Bozen-Bolzano Bolzano Italy João Paulo Almeida Federal University of Espírito Santo Vitoria Brazil Rodrigo Magalhães Kuwait Maastricht Business School Kuwait Kuwait Hans Lekkerkerk Radboud University Nijmegen Nijmegen The Netherlands ISSN 1865-1348 ISSN 1865-1356 (electronic) Lecture Notes in Business Information Processing ISBN 978-3-319-57954-2 ISBN 978-3-319-57955-9 (eBook) DOI 10.1007/978-3-319-57955-9 Library of Congress Control Number: 2017938323 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
- 9. Preface The CIAO! Enterprise Engineering Network (CEEN) is a community of academics and practitioners who strive to contribute to the development of the discipline of Enterprise Engineering (EE), and to apply it in practice. The aim is to develop a holistic and general systems theory-based understanding on how to (re)design and run enterprises effectively. The ambition is to develop a consistent and coherent set of theories, models, and associated methods that: enable enterprises to reflect, in a systematic way, on how to realize improvements; and assist them, in practice, in achieving their aspirations. In doing so, sound empirical and scientific foundations should underlie all efforts and all organizational aspects that are relevant should be considered, while combining already existing knowledge from the scientific fields of information systems, software engineering, management, as well as philosophy, semiotics, and sociology, among others. In other words, the (re)design of an enterprise and the subsequent implemen- tation of changes should be the consequence of rationalized decisions that: take into account the nature and reality of the enterprise and its environment; and respect rele- vant empirical and scientific principles. Enterprises are taken to be systems whose reality has a dual nature by being simultaneously, on one hand, centrally and purposefully (re)designed, and, on the other hand, emergent in a distributed way, given the fact that, its main agents, the humans that are the pearls of the organization, act with free will, in a creative and in a responsible (or sometimes not) way. We acknowledge that, in practice, the develop- ment of enterprises is not always a purely rational/evidence-based process. As such, we believe the field of EE aims to provide evidence-based insights into the design and evolution of enterprises and the consequences of different choices irrespective of the way decisions are made. The origin of the scientific foundations of our present body of knowledge is the CIAO! Paradigm (Communication, Information, Action, Organization) as expressed in our Enterprise Engineering Manifesto and the paper: “The Discipline of Enterprise Engineering.” In this paradigm, organization is considered to emerge in human com- munication, through the intermediate roles of information and action. Based on the CIAO! Paradigm, several theories have been developed, and are still being proposed. They are published as technical reports. The CEEN welcomes proposals of improvements to our current body of knowledge, as well as the inclusion of compliant and alternative views, always keeping in mind the need to maintain global systemic coherence, consistency, and scientific rigor of the entire EE body of knowledge, as a prerequisite for the consolidation of this new engineering discipline. Yearly events like the Enterprise Engineering Working Con- ference and associated Doctoral Consortium are organized to promote the presentation of EE research and application in practice, as well as discussions on the contents and current state of our body of theories and methods.
- 10. Since 2005 the CEEN has organized the CIAO! Workshop and, since 2008, its proceedings have been published as Advances in Enterprise Engineering in the Springer LNBIP series. From 2011 on, this workshop was replaced by the Enterprise Engineering Working Conference (EEWC). This volume contains the proceedings of the 7th EEWC, held in Antwerp, Belgium. There were 40 submissions. Each sub- mission was reviewed by three Program Committee members and the decision was to accept 12 full papers and 4 short papers, which were carefully reviewed and selected for inclusion in this volume. The EEWC aims at addressing the challenges that modern and complex enterprises are facing in a rapidly changing world. The participants of the working conference share a belief that dealing with these challenges requires rigorous and scientific solu- tions, focusing on the design and engineering of enterprises. The goal of EEWC is to stimulate interaction between the different stakeholders, scientists as well as practi- tioners, interested in making EE a reality. May 2017 David Aveiro Robert Pergl Giancarlo Guizzardi João Paulo Almeida Rodrigo Magalhães Hans Lekkerkerk VI Preface
- 11. Organization EEWC 2017 was the seventh Working Conference resulting from a series of successful CIAO! Workshops and EEWC Conferences over the last years. These events were aimed at addressing the challenges that modern and complex enterprises are facing in a rapidly changing world. The participants in these events share the belief that dealing with these challenges requires rigorous and scientific solutions, focusing on the design and engineering of enterprises. This conviction has led to the effort of annually organizing an international working conference on the topic of enterprise engineering, in order to bring together all stakeholders interested in making enterprise engineering a reality. This means that not only scientists are invited, but also practitioners. Next, it also means that the conference is aimed at active participation, discussion, and exchange of ideas in order to stimulate future cooperation among the participants. This makes EEWC a working conference contributing to the further development of enterprise engineering as a mature discipline. The organization of EEWC 2017 and the peer review of the contributions to the conference were accomplished by an outstanding international team of experts in the fields of enterprise engineering. The organizational structure of EEWC 2017 is listed herein. Advisory Board Antonia Albani University of St. Gallen, Switzerland Jan Dietz Delft University of Technology, The Netherlands Conference Chairs Jan Verelst University of Antwerp, Belgium Henderik A. Proper Luxembourg Institute of Science and Technology, Luxembourg Program Chairs David Aveiro University of Madeira and Madeira Interactive Technologies Institute, Portugal Robert Pergl Czech Technical University in Prague, Czech Republic
- 12. Session Chairs Foundational Ontologies Giancarlo Guizzardi Free University of Bozen-Bolzano, Italy João Paulo Almeida Federal University of Espírito Santo, Brazil Organizational Design Rodrigo Magalhes Kuwait Maastricht Business School, Kuwait Hans Lekkerkerk Radboud Universiteit Nijmegen, The Netherlands Organizing Chair Jan Verelst University of Antwerp, Belgium Program Committee Alberto Silva INESC and University of Lisbon, Portugal Carlos Mendes University of Lisbon, Portugal Christian Huemer Vienna University of Technology, Austria Duarte Gouveia University of Madeira, Portugal Eduard Babkin Higher School of Economics, Nizhny Novgorod, Russia Fernanda Araujo Baiao UNIRIO, Brazil Florian Matthes Technical University Munich, Germany Frank Harmsen Maastricht University and Ernst & Young Advisory, The Netherlands Frederik Gailly Ghent University, Belgium Geert Poels Ghent University, Belgium Giancarlo Guizzardi Free University of Bozen-Bolzano, Italy Gil Regev École Polytechnique Fédérale de Lausanne, Switzerland Graham McLeod University of Cape Town and Inspired.org, South Africa Hans Mulder University of Antwerp, Belgium Jan Dietz Delft University of Technology, The Netherlands Jan Hoogervorst Sogeti Netherlands, The Netherlands Jens Gulden University of Duisburg-Essen, Germany Joop de Jong Mprise, The Netherlands Jose Tribolet INESC and University of Lisbon, Portugal Joseph Barjis Institute of Engineering and Management, San Francisco, USA Julio Nardi Federal Institute of Espírito Santo, Brazil Junichi Iijima Tokyo Institute of Technology, Japan Linda Terlouw Delft University of Technology, The Netherlands Luiz Olavo Bonino VU University of Amsterdam, The Netherlands Marcela Vegetti Universidad Tecnológica Nacional, Argentina VIII Organization
- 13. Martin Cloutier Université du Québec à Montréal, Canada Martin Op ’T Land Capgemini, The Netherlands Mauricio Almeida Federal University of Minas Gerais, Brazil Miguel Mira Da Silva INESC and University of Lisbon, Portugal Monika Kaczmarek University Duisburg Essen, Germany Nelson King Khalifa University, United Arab Emirates Niek Pluijmert INQA Quality Consultants, The Netherlands Peter Loos University of Saarland, Germany Petr Kremen Czech Technical University in Prague, Czech Republic Philip Huysmans University of Antwerp, Belgium Ricardo Falbo Federal University of Espírito Santo, Brazil Robert Lagerström KTH Royal Institute of Technology, Sweden Robert Pergl Czech Technical University in Prague, Czech Republic Robert Winter University of St. Gallen, Switzerland Rodrigo Magalhaes Kuwait Maastricht Business School, Kuwait Rony Flatscher Wirtschaftsuniversität Wien, Austria Sérgio Guerreiro INESC and University of Lisbon, Portugal Sanetake Nagayoshi Shizuoka University, Japan Steven van Kervel Formetis, The Netherlands Sybren de Kinderen University of Luxembourg, Luxembourg Tatiana Poletaeva Higher School of Economics, Nizhny Novgorod, Russia Ulrik Franke Swedish Defense Research Agency, Sweden Organization IX
- 14. Contents Formalisms Formal Specification of DEMO Process Model and Its Submodel: Towards Algebra of DEMO Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Tetsuya Suga and Junichi Iijima A DEMO Machine - A Formal Foundation for Execution of DEMO Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Marek Skotnica, Steven J.H. van Kervel, and Robert Pergl Standards and Laws Adding Quality of Information to the Ontological Model of an Enterprise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Ron Deen, Johan Mijs, and Martin Op ’T Land DEMO/PSI Theory and the Law of the Land . . . . . . . . . . . . . . . . . . . . . . . 50 Duarte Gouveia and David Aveiro The Perspectives of DEMO Application to COSO Internal Audit Framework Risks Mitigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Eduard Babkin, Pavel Malyzhenkov, and Fabrizio Rossi VISI Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Niek J. Pluijmert Business Processes Converting DEMO PSI Transaction Pattern into BPMN: A Complete Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Ondřej Mráz, Pavel Náplava, Robert Pergl, and Marek Skotnica DEMO Business Processes Design to Improve the Enterprise Business Continuity Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 José Brás and Sérgio Guerreiro Normalized Systems and Evolvability Investigating the Evolvability of Financial Domain Models . . . . . . . . . . . . . 111 Marjolein Deryck, Ondrej Dvořák, Peter De Bruyn, and Jan Verelst
- 15. Exploring Design Aspects of Modular and Evolvable Document Management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Gilles Oorts, Herwig Mannaert, and Peter De Bruyn Application of Enterprise Engineering to Lean Process Management: An Explorative Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Marjolein Deryck and Philip Huysmans Ontologies The REA Model Expressed in a Generic DEMO Model for Co-creation and Co-production. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Frantisek Hunka and Steven J.H. van Kervel SysPRE - Systematized Process for Requirements Engineering . . . . . . . . . . . 166 Ana Neto, Duarte Pinto, and David Aveiro Revisiting the DEMO Transaction Pattern with the Unified Foundational Ontology (UFO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Tanja Poletaeva, Giancarlo Guizzardi, João Paulo A. Almeida, and Habib Abdulrab Organisation Design An OD-Pearl for the EE-Oyster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 L.J. Lekkerkerk A Literature Review of Coordination Mechanisms: Contrasting Organization Science and Information Systems Perspectives . . . . . . . . . . . . . 220 Maximilian Brosius, M. Kazem Haki, Stephan Aier, and Robert Winter Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 XII Contents
- 16. Formalisms
- 17. Formal Specification of DEMO Process Model and Its Submodel Towards Algebra of DEMO Models Tetsuya Suga(B) and Junichi Iijima Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan {suga.t.ac,iijima.j.aa}@m.titech.ac.jp Abstract. This paper discusses a specification and merge operation over submodels of a given Process Model (PM) in Design and Engineering Methodology for Organizations (DEMO). In general, a submodel is a part of a given model. An earlier work proposed how submodels of a given DEMO Construction Model (CM) can be attained by a set-theoretic for- malization. However, it remains unclear how to expand the formalism to the notion of submodels of a given PM. Since the given PM should align with the corresponding CM, a submodel of the given PM should not only be a PM, but also conform to the corresponding submodel of the CM. These two independent constraints indicate the desired defini- tion and formalization of submodels of PMs. The proposed approach is shown to be applicable to a common demonstration case. Through the formalization, this paper shows the closure, commutativity, and associa- tivity of the merge operation over submodels of a given PM. Moreover, it is found that the consistency between CMs and PMs is preserved during the merge operation. Keywords: Enterprise ontology · Merge · Algebra · DEMO process model · Match 1 Introduction In recent years, organizations have been objects of interest in a variety of disci- plines, not only in social science and business administration, but also in engi- neering. Enterprise engineering (EE) is an emerging discipline of systems engi- neering that studies organizations from an engineering perspective [1]. Since Enterprise Ontology provides models of enterprises with considerably reduced complexity [2], a (re)design process with such a methodology inevitably requires working with a model of the organization rather than the real-world organization itself. Put another way, (re)designing an enterprise is substantially achieved by building and editing models of the enterprise, and implementing the changes in the model in the real world. c Springer International Publishing AG 2017 D. Aveiro et al. (Eds.): EEWC 2017, LNBIP 284, pp. 3–17, 2017. DOI: 10.1007/978-3-319-57955-9 1
- 18. 4 T. Suga and J. Iijima A vast majority of the work in this area has focused on artifacts in the category of Way of Thinking (WoT), Way of Modeling (WoM), and Way of Working (WoW) in five ways in information system methodologies [3], such as artifacts that are typically involved in the process of modeling. There is, however, relatively limited research investigating theories that may support the process of manipulating models, a possible contribution to Way of Supporting (WoS). In particular, the requirements of submodels of enterprise models and operations over the submodels remain unclear. In this article, a submodel is a part of a given model that has been already created. The given model is often called the global model. Submodels are used for diverse reasons and purposes, such as to partition the enterprise, to focus on only some part in question, to hide some part for readability or even because of an access control policy, and so on. Logically speaking, regardless of the reasons, the requirements of those partial models of enterprise models should be specified if we rigidly define what “part of” means. Unless they are defined properly, we might allow submodels that do not conform to preconditions of the global model, including (but not limited to) its metamodel. An operation over one or more models (i.e., inputs) means creating another model by input model(s). Once the requirements of submodels have been established, we may leverage those sub- models by considering operations over the submodels such as merge submodels. Such operations may include merge, diff, split, slice, and so forth. Again, if we do not define the operation rigorously, we might get a model that does not conform to the requirements of the global model as a result of performing the operation. In addition, we should study and then be aware of properties of the operation such as the associative and the commutative properties. Insufficient investigation of the formalization and manipulability of enterprise models, i.e., a scarcity in WoS, stands in the way of the success of EE in the market. Presently, such a model manipulation and the following model checking require manual work by professionals with considerable expertise not only in the business, per se, but also in the modeling framework and theories behind it. However a certain part of the work could be taken over or even rendered unnecessary by formalization and automation with computer-aided design tools. Other disciplines, such as mechanical engineering, electrical engineering, and computer science, demonstrate the successful implementation of computer-aided design tools and automation. Therefore, this research aims at investigating the structure and properties in submodels and operations in DEMO PMs based on an earlier work on those in DEMO CMs. Although the earlier work established the formalization of CMs, PMs are characterized by components that are specific to PMs, such as process step kinds and causal/waiting links. Another requirement for the formalization of PMs is to capture the relationship between a CM and a PM when they are integrated in one DEMO model. In this article, we say that a Process Structure Diagram (PSD, a representation of a PM) is matched to an Organization Con- struction Diagram (OCD, a representation of CMs) as defined formally later in Definition 13.
- 19. Formal Specification of DEMO Process Model and Its Submodel 5 We first propose an algebraic structure of a PSD and its submodels. In this step, we use the set-theoretic formalization and encode the structure of a DEMO PSD. It is because, as the earlier work [4] extensively discussed, other forms of formalism such as Z notation, temporal logic, description logics, and category theory turn out to be inappropriate for the purpose of the study. Those existing formalisms not only have different structures in modularity than DEMO PSDs, but are also inadequate for algebraic construction. In addition, it is beneficial to use the same type of formalism with the earlier work on CMs to leverage the knowledge and findings there. Although a PM specifies the state and transition space of the coordination world, it seems enough to rely on the set-theoretic formalism as long as we follow the metamodel. Secondly, an operation over the structure, the “merge” operation, is defined and associated properties are exam- ined by formal proofs. Then, we consider a pair-wise merge operation for OCDs and PSDs. The result corroborates the coherence and consistency of DEMO mod- els from a different angle. Towards the ultimate goal of constructing the algebra of DEMO models, including four aspect models, the current research project has worked on the algebra of PSDs. This article reports preliminary findings of the ongoing research, which captures a DEMO PSD as a static object. The remainder of this paper is composed as follows. In the next chapter, we provide an overview of the background concepts and previous works related to the issue addressed in this article. The main result is given for the construction of an algebraic structure for DEMO PMs and an algebra over the structure, in Sects. 3 and 4, respectively. Section 5 discusses the contribution and limitations of this work, and concludes with a look at future directions. 2 Literature Review 2.1 Background Concepts DEMO. Design Engineering Methodology for Organizations (DEMO) is a modeling methodology for enterprises [2]. Although an enterprise—as an abstract term referring to (an assembly of) collaborative activities by human beings— has two perspectives (i.e., function and construction) in terms of systems engi- neering, DEMO spotlights the construction perspective. In addition to its focus on the construction of enterprises, DEMO also emphasizes the communications within enterprises, namely from the language/action perspective. For detailed information about DEMO, we refer the reader to [1,2]. DEMO is more suitable for the purpose and procedures of this research than other enterprise modeling languages, including business process modeling lan- guages. It is because it provides a strong connection between the syntax and semantics. As shown in the rest of this article, elements of DEMO models are formalized by mathematics and studied from their isomorphic mathematical rep- resentations rather than the DEMO models themselves. Therefore, the strong connection is beneficial and essential to ensure the alignment between meanings (semantics) and symbols (syntax) when we encode DEMO models to mathemat- ical representations and decode them back.
- 20. 6 T. Suga and J. Iijima Aspect Models. The ontological model of an enterprise is represented by four aspect models, which each reflect a specific aspect of the enterprise. Because of the interest of this paper, we elaborate the Process Model here. The Process Model (PM) of an enterprise specifies the state and transition space (i.e., the set of lawful sequences of the states) of the coordination world. Those states and transitions are largely specified by the universal transaction pattern. A PM is expressed in a Process Structure Diagram (PSD) for the whole and a Transaction Pattern Diagram (TPD) for each transaction kind. Although “exception(s)” dealt with in the model can be only specified in the TPD, the PSD occupies the central role in the PM. In other words, if we limit ourselves to a happy path, a PSD can be regarded as a PM without a TPD. Therefore, as a first attempt, this work concentrates on PSDs in the rest of this article. Figure 1a shows an example of a PSD. We use this metamodel as the grounds of the formalization of PSDs. Fig. 1. DEMO PM Abstract Algebra. Set theory and structure jointly play significant roles in mathematics. Intuitively, a set is simply a collection of objects known as ele- ments that exist without any relation to each other. In contrast, a structure is a set together with some relations among elements of the set. Informally, such a structure is defined by specifying the elements and the relations. The rest of this section introduces an algebraic structure, which is one of well-known structures established by mathematicians. Algebraic Structure. In abstract algebra, an algebraic structure consists of a set (called an underlying set), with one or more operations defined on the set, that satisfies certain axioms. The structure enables us to formalize and analyze objects that are more complex than just a collection of objects. Schematically, an algebraic structure is specified as a pair A; F, where A is an underlying set and F is a family of finitary operations on A. Although we often assume the axioms of set theory, we may add or modify the axioms to shape the structure in order to represent more complex systems and allow derivations. A set is an instance of such an algebraic structure with F being empty (i.e., A; ∅), whereas there are well-known variants such as groups, rings, lattices, and so on.
- 21. Formal Specification of DEMO Process Model and Its Submodel 7 Algebra of Structures. Now we rise to a meta-level and introduce an algebra of (over) a structure. In the case of a set as a simple structure, the algebra of sets defines the laws over sets, the relations over sets (e.g., equality and inclusion), and set-theoretic operations over sets (e.g., union, intersection, and complement). Similarly, one may construct an algebra of an arbitrary structure. The ultimate goal of this research is to construct an algebra of DEMO models. 2.2 Related Works Except for an earlier work [4], there exist very few formalizations for DEMO models, namely the CRISP model [6], Petri Nets [7,8], and XML schema [9]. Though we do not repeat the details of evaluations and insufficiency of those formalizations as a solution for the issue targeted by this research, the main deficiencies of the existing approaches are that none of them provide algebraic operations to form any type of algebra [4]. Since, this present work is dependent on the formalization of DEMO OCDs in the earlier work, we recall the essen- tial definitions and theorem here. The full descriptions, including proofs and rationale, are available in [4]. Algebraic Structure of DEMO OCD. An algebraic structure of a DEMO OCD is defined by elements of sets and associated operations over the sets. Definition 1 (Society). A society S = A, T, as a universe, is made up of a set of actor roles A and a set of transaction kinds T. Definition 2 (Actor Role). An actor role has the following mappings: 1. fARno : A → N0 represents the number of each actor role, and 2. fARname : A → string represents the name of each actor role. Definition 3 (Transaction Kind). A transaction kind t is a pair of actor roles (a, a ), where a and a are called an initiator and an executor, respectively1 . Formally, t ∈ A × A. Transaction kinds have the following mappings: 1. fT no : T → N+ represents the number of each transaction kind, 2. fT name : T → string represents the name of each transaction kind, 3. fT in : T → A represents the initiator of each transaction kind, 4. fT ex : T → A represents the executor of each transaction kind. Definition 4 (OCD). Given that A is a subset of A, and T is a subset of T, an OCD is a pair A, T ∈ 2A × 2T that satisfies the following conditions: Condition 1 (Unique Actor Role Name). ∀ai, ∀aj ∈ A, (fARname (ai) = fARname (aj) ⇒ ai = aj) Condition 2 (Unique Transaction Kind Name). ∀ti, ∀tj ∈ T, (fT name (ti) = fT name (tj) ⇒ ti = tj) 1 [4] assumes that there is only one initiator for each transaction kind.
- 22. 8 T. Suga and J. Iijima Condition 3 (Numbering Convention). ∀t ∈ T, fARno (fT ex (t)) = fT no (t) Condition 4 (Closure for Actor Role). ∀t ∈ T, ∀a ∈ ActorRole, a ∈ fT in (t) ∪ fT ex (t) ⇒ a ∈ A Condition 5 (Actor Role Participation). ∀a ∈ A, ∃t ∈ T, a ∈ fT in (t) ∪ fT ex (t) Based on this algebraic structure, we define the notion of “submodel” of a given OCD with the following formal specification. Definition 5 (Sub-OCD). Given an OCD A◦ , T◦ , a couple A, T is said to be “a sub-OCD of A◦ , T◦ ” if A, T is an OCD (i.e., satisfies Definition 4), and A ⊆ A◦ and T ⊆ T◦ hold. Algebra of DEMO OCDs. Toward the algebra of DEMO OCDs, the previous work [4] introduced an operation over sub-OCDs of a given global OCD which performs the merger of the two sub-OCDs. Here we repeat the definition and its behavior as formulated in the form of theorems. Definition 6 (OCD Merge). Given an OCD A◦ , T◦ and its two sub-OCDs AX, TX and AY , TY , the merge operation ∇ : 2A × 2T × 2A × 2T → 2A × 2T is defined as AX, TX ∇ AY , TY AX ∪ AY , TX ∪ TY . Theorem 1. The family of sub-OCDs of a given OCD is closed under the merge operation ∇. Theorem 2. The merge operation ∇ is commutative and associative in the fam- ily of sub-OCDs of a given OCD. Relationship Between a CM and a PM. Although the specification of DEMO [5] specifies the metamodels for each aspect model separately, with less attention to the relationship between them, there are a few articles that address the relationship to ensure the integrity of the four aspect models. Particularly, we use [9] as a reference, which elaborates the requirements for transformation from a CM to a PM with coherence and consistency as “transformation rules”. 3 Construction of Algebraic Structure This section provides a formalization of the DEMO PSD and its submodels, which serves as the rigorous foundation for this research. We use a common case study of Pizzeria [2] as a running example throughout this paper. For convenience, the PSD of Pizzeria is repeated in Fig. 2. Although it is a convention to draw actor roles with swim lanes, we omit them because they are not included in the metamodel of the PM.
- 23. Formal Specification of DEMO Process Model and Its Submodel 9 3.1 PSD and Its Submodels Algebraic Structure of PSD. As noted by the metamodel of the DEMO PM in Fig. 1b, the PSD has transaction kinds (TK), process step kinds (PSK), and transaction process step kinds (TPSK) as its components, with causal links and conditional links (denoted as “TK is an initiated from TPSK” and “TPSK is a wait condition for [another] TPSK”, respectively). As a natural and straightfor- ward approach, these components and links are formalized as sets and relations, respectively, below. Let T be a set of transaction kinds. Transaction kinds have mappings to provide the name and number, namely fT name : T → string and fT no : T → N. This definition is to give a universe, which contains all the entities we may wish to consider in a given situation. Thus, this set is not restricted to transaction kinds in a particular enterprise under consideration. I is a set of process step kinds, which consists of Production-acts and Coordination-acts, namely I = {rq, pm, ex, st, ac} in the case of the basic trans- action pattern2 . Since the static structure is of interest in the formalization, it is enough for I to be a set within the scope of this article. If the dynamic aspect in timing is considered, I should be accompanied by an order relation. Based on the notations introduced so far, (t, i) ∈ T × I denotes a transac- tion process step kind, as specified in the metamodel by an aggregation of a transaction kind and a process step kind. Example 1. Suppose we decide to consider Pizzeria as a given DEMO model. As it is a convention that sets and relations for the given global model are indicated by a circle ◦ in the superscript, the OCD of Pizzeria is denoted as A◦ , T ◦ , and the PSD is denoted as T◦ , V ◦ , W◦ . In the scope of Pizzeria, we identify four transaction kinds: T1, T2, T3, and T4. We use t with the corresponding index to refer to these transactions kinds. Thus, the set of transaction kinds is T = {. . . , t1, t2, t3, t4, . . .}. As clarified in Sect. 3.1, “. . .” is intentionally placed to express that T is a universe, and hence may include other transaction kinds. Fig. 2. PSD of Pizzeria 2 When the formalization is expanded to the standard transaction pattern, I equals {rq, pm, ex, st, ac, dc, qt, rj, sp}.
- 24. 10 T. Suga and J. Iijima In the universe of transaction kinds, we create the set of transaction kinds for Pizzeria T◦ ⊆ T as T◦ = {t1, t2, t3, t4} . According to the names of the transaction kinds in Pizzeria, we have fT name : t1 → “completion”, t2 → “preparation”, t3 → “payment”, t4 → “delivery”. Based on this configuration, a transaction process step kind request of T1, for instance, is encoded into (t1, rq) ∈ T × I. Definition 7 (Activation Relation). Let V be a relation over (T × I) × T, where ((t, i) , t ) ∈ V represents that a transaction kind t is activated from a transaction process step kind (t, i). In this case, V is called an activation relation over T. Example 2. The PSD of Pizzeria has three causal links from the promise of T1 to T2, T3 and T4. In our formalism these are expressed by the relation V ⊆ (T × I) × T. Thus, the relation for causal links in Pizzeria V ◦ ⊆ V is V ◦ = {((t1, pm) , t2) , ((t1, pm) , t3) , ((t1, pm) , t4)} . Definition 8 (Wait Relation). Let W be a relation over (T × I) × (T × I), where ((t, i) , (t , i )) ∈ W represents that a transaction process step kind (t , i ) is a wait condition for a transaction process step kind (t, i). In this case, W is called a wait relation over T. Example 3. The PSD of Pizzeria also specifies three conditional links from the accept of T2 to the execute of T4, from the accept of T4 to the request of T3, and from the accept of T3 to the execute of T1. These are encoded into the relation W ⊆ (T × I) × (T × I). In Pizzeria, W◦ ⊆ W is W◦ = {((t2, ac) , (t4, ex)) , ((t4, ac) , (t3, rq)) , ((t3, ac) , (t1, ex))} . Just for the purpose of labeling, we define a Transaction Process Step net (TPS- net), which is a triple-wise subset of a given tuple of sets as defined below. Definition 9 (TPS-net). A TPS-net is a triple T, V, W, where T is a subset of T, V is a subset of V, and W is a subset of W. Definition 10 (PSD). Given that T is a subset of T, V is a subset of V, and W is a subset of W, a PSD is a TPS-net T, V, W that satisfies3 Property 1. ∀ti, tj ∈ T, (fT name (ti) = fT name (tj) =⇒ ti = tj), Property 2. ∀ ((t, i) , t ) ∈ V, t ∈ T ∧ t ∈ T, and Property 3. ∀ ((t, i) , (t , i )) ∈ W, t ∈ T ∧ t ∈ T. 3 Although it is possible to impose more constraints such as “a wait condition must bridge two distinct transaction kinds”, we aim for fidelity to the metamodel.
- 25. Formal Specification of DEMO Process Model and Its Submodel 11 In plain English, the first property imposes the uniqueness of the names of transaction kinds as name equivalence; the second and third properties ensure the source and target transaction kinds of a link are included in the PSD. By definition, any PSD of T, V, W is also a TPS-net. As we assume the basic transaction pattern in this article, we do not explicitly write I. Example 4. It is easily confirmed that the tuple T◦ , V ◦ , W◦ satisfies the definition of a PSD. Algebraic Definition of PSD Submodels. So far, we have described the formalism for PSDs. Here we proceed to define the notion of submodels for PSDs. Definition 11 (Sub-TPS-net). Given two TPS-nets T, V, W and T , V , W , T , V , W is said to be a sub-TPS-net of T, V, W if T ⊆ T, V ⊆ V , and W ⊆ W. Accordingly, we define “the family of sub-TPS-nets brought by a given PSD T, V, W” that is the collection of all the TPS-nets T , V , W that are sub- TPS-nets of T, V, W. We use ℘ (T, V, W) as a shorthand form for the family of sub-TPS-nets of T, V, W. Definition 12 (Sub-PSD). Given a PSD T, V, W, a TPS-net T , V , W is said to be a sub-PSD of T, V, W if T , V , W is a sub-TPS-net of T, V, W and a PSD (i.e., it satisfies the three properties in Definition 10). Accordingly, we define “the family of sub-PSDs brought by a given PSD T, V, W” that is the collection of all the PSDs T , V , W that are sub-PSDs of T, V, W. We use P (T, V, W) as a shorthand form for the family of sub-PSDs of T, V, W. Example 5. Figure 3a illustrates one member of the family of sub-TPS-nets made by the given PSD. As the diagram notes, this is broken in the sense that the causal link from the promise of T1 to T2, but T2 is not included in Fig. 3a. Let T0, V0, W0 denote this diagram. Since T0 = {t1, t4} ⊆ T◦ , V0 = {((t1, pm) , t2) , ((t1, pm) , t3)} ⊆ V ◦ , and W0 = {((t3, ac) , (t1, ex))} ⊆ W◦ , T0, V0, W0 is a sub-TPS-net of the given PSD according to Definition 11. How- ever, this is not a sub-PSD of the given PSD due to the second property of Definition 12 not being satisfied. In contrast, Fig. 3b is a sub-PSD of the given PSD. Although this definition requires a sub-PSD to satisfy the three conditions in Definition 10, we have to ensure only the second and third properties because of the following proposition. For readability, all proposition and theorem proofs are detailed in the Appendix. Proposition 1. Given a PSD T◦ , V ◦ , W◦ , any member of the family of sub- TPS-nets ℘ (T◦ , V ◦ , W◦ ) satisfies the following condition: Property 1. ∀ti, tj ∈ T, (fT name (ti) = fT name (tj) =⇒ ti = tj)
- 26. 12 T. Suga and J. Iijima Fig. 3. Example in Pizzeria 3.2 Match Between a CM and a PM Independent of Sect. 3.1, this section describes another angle to restrict the free- dom in a formalized PSD in terms of its coherence and consistency to the corre- sponding CM. Based on previous work [9, Chaps. 4 and 7], the requirements are shaped as (1) the set of transaction kinds in the PSD equals that in the OCD (up to name equivalence), and (2) the causal links between transaction kinds in the PSD should reflect the product structure of the OCD. These are formally defined as follows: Definition 13 (Match). Given an OCD A, T , a PSD T, V, W is said to be matched to the OCD if 1. T = T, and 2. ∀t, t ∈ T , (∃a ∈ A, fex (t) = a = fin (t )) ⇐⇒ (∃i ∈ I, ((t, i) , t ) ∈ V ). In this case, we may say an OCD and a PSD are matched. The second condition above states the PSD is aligned to the product structure of the enterprise. Notably, based on our formalism, the product structure is uniquely derived from the OCD. Precisely speaking, the OCD can be uniquely transformed to the tree of organizational building blocks, and then uniquely converted to the tree of the product structure. According to the composition axiom [2], a root node is uniquely identified by a transaction kind that is initiated by the environmental actor role, or initiated by its executor itself (i.e., a self- activated transaction kind). In a simple case such as Pizzeria, the product struc- ture is said to be a tree, which has one root transaction. The product structures of more complex cases, including Library [2], must be a collection of trees with sharing. The directed adjacency relation between transaction kinds, written as R ⊆ T × T , is uniquely obtained as R = {(t, t ) | ∃a ∈ A, fex (t) = a = fin (t )}. 4 Algebra of PSDs This section introduces an operation and explores its properties. As the first step, we define the “merge” operation for two sub-PSDs of a given PSD. Then,
- 27. Formal Specification of DEMO Process Model and Its Submodel 13 in association with the merge operation of the OCD proposed in the earlier work (see Sect. 2.2), we elaborate the behavior of the DEMO OCD and PSD during the “merge” operation. 4.1 Merge Operation on Sub-PSDs Analogous to set-theoretic union, the merge operation takes two sub-PSDs of a given PSD and produces an output that contains the two input models— specifically, the two sub-PSDs shall be a part (submodel) of the output, as for- mulated below. Definition 14 (PSD Merge). Given a PSD T◦ , V ◦ , W◦ and its two sub- PSDs TX, VX, WX and TY , VY , WY , the merge operation : 2T × 2V × 2W × 2T × 2V × 2W → 2T × 2V × 2W is defined as TX, VX, WX TY , VY , WY TX ∪ TY , VX ∪ VY , WX ∪ WY . Example 6. Finally, we demonstrate the merge operation using the sub-PSDs (Figs. 4a and b) of the given PSD in Fig. 2 to obtain the result in Fig. 4c. The sub-PSD in Fig. 4a is encoded as T1, V1, W1 = {t1, t3} , {((t1, pm) , t3)} , {((t3, ac) , (t1, ex))} and in Fig. 4b as T2, V2, W2 = {t1, t2} , {((t1, pm) , t2)} , ∅. Then, the merged PSD in Fig. 4c is obtained by Definition 14 as T1, V1, W1 T2, V2, W2 = {t1, t3}∪{t1, t2} , {((t1, pm) , t3)}∪{((t1, pm) , t2)} , {((t3, ac) , (t1, ex))} ∪ ∅ = {t1, t2, t3} , {((t1, pm) , t3) , ((t1, pm) , t2)} , {((t3, ac) , (t1, ex))}. Based on this definition, we claim three notable properties. First, the result of the operation is indeed a sub-PSD of the given PSD. Furthermore, this operation frees users from concerns about the order of the input models; changing the order of inputs does not change the result. These properties are formulated in theorems. T1, V1, W1 T2, V2, W2 = Fig. 4. PSD merge in Pizzeria Theorem 3. The family of sub-PSDs of a given PSD T◦ , V ◦ , W◦ is closed under the merge operation , i.e., ∀ TX, VX, WX , TY , VY , WY ∈ P (T◦ , V ◦ , W◦ ), TX, VX, WX TY , VY , WY ∈ P (T◦ , V ◦ , W◦ ) .
- 28. 14 T. Suga and J. Iijima Theorem 4. The merge operation is commutative and associative on the family of sub-PSDs of a given PSD T◦ , V ◦ , W◦ , i.e., ∀ TX, VX , WX , TY , VY , WY , TZ, VZ, WZ ∈ P (T◦ , V ◦ , W◦ ), TX, VX, WX TY , VY , WY = TY , VY , WY TX, VX , WX and (TX, VX, WX TY , VY , WY ) TZ, VZ, WZ = TX, VX , WX (TY , VY , WY TZ, VZ, WZ) . 4.2 Preserved Match Between the OCD Merge and PSD Merge In addition to the behavior of the PSD merge as discussed so far, we claim the final theorem in this article guarantees the consistency between the PSD merge and OCD merge, as illustrated in Fig. 5. X , TX Y , TY X , TX Y , TY TX , VX , WX TY , VY , WY TX , VX , WX TY , VY , WY match match match? Fig. 5. Illustration of Theorem 5 Theorem 5. Given an OCD A◦ , T ◦ and a matched PSD T◦ , V ◦ , W◦ , let AX, TX and AY , TY be sub-OCDs of the given OCD and TX, VX, WX and TY , VY , WZ be sub-PSDs of the given PSD. If TX, VX, WX is matched to AX, TX and TY , VY , WY is matched to AY , TY , the result of the PSD merge is matched to the result of the OCD merge, i.e., TX, VX , WX TY , VY , WY is matched to AX, TX ∇ AY , TY . Practitioners may take advantage of this theorem. A project to merge two sub- OCDs and sub-PSDs can be divided into four smaller tasks as follows: (1) ensure one sub-PSD is matched to one sub-OCD, (2) ensure the other sub-PSD is matched to the other sub-OCD, (3) merge the two sub-OCDs, and (4) merge the two sub-PSDs. The four tasks can be completed separately by different indi- viduals and/or computers without collaboration. Moreover, nobody has to check whether the result of task 4 (PSD merge) is matched to the result of task 3 (OCD merge) because it is guaranteed by this theorem.
- 29. Formal Specification of DEMO Process Model and Its Submodel 15 5 Conclusion and Future Research The goal of this paper was to present a straightforward construction of an alge- braic structure for DEMO PSDs and explore the merge operation as an instance of model manipulations. The primary result states that the family of sub-PSDs of a given PSD is closed under the merge operation, while preserving the integrity of sub-OCDs and sub-PSDs. Furthermore, the merge operation is commutative and associative in that family. Stated another way, the finding may reinforce the coherence and consistency of DEMO from a different angle. The contribution of this work is not limited to the theoretical aspect, is but of significance to practitioners as well. The commutativity and associativity of the merge operation ensure the same result regardless of the order of the operations. If one wishes to merge three models, A, B, and C but B is not available yet, one can first merge A and C, then merge the result and B later when B becomes available. Moreover, Sect. 4.2 exhibits the contribution of this work in terms of division of labor in a practical scenario. As we mentioned in Sect. 1, these for- mal specifications of DEMO aspect models and investigation of mathematical behavior should provide a solid foundation of computer-aided design environ- ments, which may play an important role in the future development of Way of Supporting, which has attracted less attention so far, but will be of significance in Enterprise Engineering. Although this research has answered the issue addressed in Sect. 1, there is an intrinsic limitation in that the formalization only captures the static aspect of DEMO PMs. Considering each transaction kind is a finite state machine (FSM) in the sense of the universal transaction pattern, a PM is a composition of FSMs. Thus, this paper ignores dynamic aspects such as the behavior of the composite FSMs and may miss some important points. In fact, the authors noticed that a PSD in Fig. 6b is intuitively and realistically a good submodel of a given PSD in Fig. 2 in the sense that the accept of T4 is a waiting condition for the execute of T1, particularly when you interpret the purpose of making submodels is to ignore one or more specific transaction kinds. However, the PSD in Fig. 6b is invalid in the presented formalization because the waiting condition in question is not included in the given global PSD. This observation implies that the formalization could be improved, probably by revising the definition of part of to reflect the dynamic aspects. This limitation also implies more case studies are required for further validation. Fig. 6. Two Sub-PSDs
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- 34. The Project Gutenberg eBook of The Romance of War; or, The Highlanders in Spain, Volume 3 (of 3)
- 35. This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook. Title: The Romance of War; or, The Highlanders in Spain, Volume 3 (of 3) Creator: James Grant Release date: June 15, 2017 [eBook #54920] Language: English Credits: Produced by Al Haines *** START OF THE PROJECT GUTENBERG EBOOK THE ROMANCE OF WAR; OR, THE HIGHLANDERS IN SPAIN, VOLUME 3 (OF 3) ***
- 36. THE ROMANCE OF WAR: OR, THE HIGHLANDERS IN SPAIN BY JAMES GRANT, ESQ. Late 62nd Regiment. In the garb of old Gaul, with the fire of old Rome, From the heath-covered mountains of Scotia we come; Our loud-sounding pipe breathes the true martial strain, And our hearts still the old Scottish valour retain. Lt.-Gen. Erskine. IN THREE VOLUMES. VOL. III. LONDON: HENRY COLBURN, PUBLISHER, GREAT MARLBOROUGH STREET. 1846.
- 37. LONDON: PRINTED BY MAURICE AND CO., HOWFORD BUILDINGS, FENCHURCH STREET. CONTENTS Chapter I. Hostilities—A Love Letter II. The Ball.—The Bull-Fight.—An Adventure III. The Skirmish of Fuente Duenna. The Leaguer of Alba de Tormes IV. Angus Mackie V. An Adventure. A Highland Legend VI. A Battle VII. An Out-Picquet Adventure VIII. Pass of Maya.—Pyrenees IX. The Block-house. Mina X. The Châtelet XI. Passage of the Nive THE ROMANCE OF WAR.
- 38. CHAPTER I. HOSTILITIES—A LOVE LETTER. Were not my right hand fetter'd by the thought, That slaying thee were but a double guilt In which to steep my soul, no bridegroom ever Stepp'd forth to trip a measure with his bride More joyfully than I, young man, would rush To meet thy challenge. Macduff's Cross, p. 26. Boiling with rage at Louis's insulting defiance, Ronald returned to his quarters in the Alcanzar, determined at day-break to summon him forth, to fight or apologize. He often repeated the words, Her heart has never wandered from you. Ah! if this should indeed be the case, and that Alice loved him after all! But from Louis, his honour demanded a full explanation and ample apology, either of which he feared the proud spirit of the other would never stoop to grant. Yet, to level a deadly weapon against the brother of Alice,—against him to whom he had been a constant friend and companion in childhood and maturer youth, and perhaps by a single shot to destroy him, the hopes and the peace of his amiable father and sister, he felt that should this happen, he never could forgive himself. But there was no alternative: it was death or dishonour. Two ways lay before him,—to fight or not to fight; and his sense of injured honour made him, without hesitation, choose the first,
- 39. and he waited in no ordinary anxiety for the dawn, when Alister Macdonald, who was absent on duty, would return to the quarters of the regiment. Next morning, when the grey daylight was beginning faintly to show the dark courts and gloomy arcades of the Alcanzar, he sprung from his couch, which had been nothing else than his cloak laid on the polished floor tiles; and undergoing a hasty toilette, he was about to set forth in search of Macdonald, when Lieutenant Chisholm, one of the officers, entered. What! up already, Stuart? said he; I hope you are not on any duty? No. Why? Because Lisle has asked me to wait upon you. Upon me? asked Ronald, with a frown of surprise. Upon me, Chisholm? Yes: of course you will remember what occurred in the cathedral last night? How could I ever forget? Mr. Lisle, under its roof, insulted me most grossly, replied Ronald, his lips growing white with anger. I was just about to seek Macdonald to give him a message, but Mr. Lisle has anticipated me. For Heaven's sake, Stuart, let us endeavour to settle this matter amicably! Think of the remorse which an honourable survivor must always feel. A hundred men slain in action are nothing to one life lost in a duel. Address these words to your principal,—they are lost on me; but you are an excellent fellow, Chisholm!
- 40. It is long since we have had an affair of this sort among us, and Cameron is quite averse to this mode of settling disputes. I shall not consult his opinion, or that of any other man, in defence of my own honour, said Ronald haughtily. As you please, replied the other, with an air of pique. Lisle and you have long been on very distant terms, and the officers have always predicted that the matter would terminate in this way. Curse their impertinent curiosity! And so Lisle calls me out in consequence of the high words we exchanged in the cathedral last night? That is one reason—the least one, I believe. He mentioned that his sister, Miss Lisle— Stay, Chisholm! I will hear no more of this, cried Stuart; then suddenly changing his mind added, Ah! well; his sister—Miss Alice Lisle. Go on. Faith, Stuart, you seem confoundedly confused. Do settle this matter in peace. Lisle has told me the story, in confidence, and I think you have been to blame,—indeed you have. Send Lisle an apology, for I assure you he is boiling with passion, and will not yield a hair's breadth. Chisholm, then how in the devil's name can you suppose that I will? exclaimed Ronald, his anger getting the better of his confusion. Never, by Heaven! never will I apologize when I have suffered the indignity. He has challenged me, and fate must now decide. I will meet him. Well, then, time presses; we march at sunrise. Who is your friend?
- 41. Alister Macdonald, if he has returned; if not, I shall have Logan. Macdonald returned about midnight with some stragglers from Torrijos, and will not relish being disturbed so early. Never mind that; an hour's sleep less or more is scarcely to be considered when lives are in jeopardy. Where is the meeting place? The bridge of Toledo. You will barely be in time. Six is the hour; it wants fifteen minutes of it by my watch. Well, you may leave me now. Knowing it was needless to say any more about a reconciliation Chisholm departed; and Ronald, after buckling on his sword and dirk, stood for a few minutes holding his bonnet in his hand irresolutely, while he sunk into a reverie of deep and bitter reflections, of what his affectionate old sire and faithful dependants at Lochisla would feel should he die by the hand of Lisle, whose very name they regarded with so much jealousy and distrust. He also thought of Alice and Lord Lisle, what their sentiments would be if the reverse was the case, and the one lost a dear brother—the other a beloved son, who was the only heir and hope of an ancient house, and the successor to its title. He remembered also the words of Louis. Could it be that Alice might yet love him? But no; that was impossible! He threw his cloak around him, and rushed from the chamber to seek that of Macdonald, who was ready to attend him in a moment. Suddenly remembering that he had no pistols, he urned into an apartment occupied by Major Campbell, to request the loan of his. It was a spacious and splendid room, with a ceiling twenty feet in height. A colonnade supported the roof, the carved beams of
- 42. which stretched across from the gilded cornices on each side. The ceiling and walls were covered with frescoes, but the plaster and the once bright and gorgeous gilding were miserably faded and dilapidated by time and neglect. Rolled in his cloak, and coiled up in a corner of this vast and empty hall, the bulky frame of Campbell lay on the tessellated pavement, and no doubt he found it a bed somewhat cold and hard. His pillow was formed by his long Andrea and favourite rung, with a plaid rolled round them. His dirk and steel Highland pistols lay on one side of him, and an empty pigskin on the other. Very desolate indeed he appeared, lying in a corner of that huge apartment, which was totally destitute of furniture. Ronald shook him by the shoulder. If that is you, Serjeant Macildhui, said he, speaking very crossly beneath the cape of his cloak, I must beg leave to inform you, that I have nothing to do now with No. 1 company. I am done with all that sort of dirty work, as you will see by the last Gazette. Apply to Mr. Kennedy, and take yourself off till the drum beats. I wish the infernal Horse Guards would order six halting days every week, instead of only Sunday and Thursday. Look up, major! 'Tis I—Stuart. What is the matter? cried the other, bolting up, and showing that the contents of the borachio skin were operating still on his brain; what is the matter now? It is very hard that a field-officer, and one too that has seen the fields of Alexandria, Egmont-op-Zee, and the onslaught of Copenhagen, should be so pestered by subalterns. How this hard bed makes my bones ache! I have slept softer on the hot yellow sand in Egypt. They tell me this was the bed-room of Don Alfonso the First, king of Castile. Devil mend him! I
- 43. suppose he did not sleep on the pavement with a claymore for a pillow, like Colin Campbell of Craigfianteoch, in Lorne, a better man —for what is any Castilian don when compared to a duine-wassal of Argyle? The major snapped his fingers, and it was evident he was very tipsy. But what do you want, Ronald, my boy? he added. The loan of your pistols, major, for ten minutes only. I have a very disagreeable affair to adjust this morning. I regret to hear it; but it is with none of ours, I hope, my knight of Santiago? This is no time for jesting. 'Tis with a Portuguese of Colonel Campbell's brigade, said Ronald, colouring at the necessary falsehood. Pah! only a Portuguese,—a dirty garlic-eating devil. There are the pistols; and remember, always level low, and fire the instant the word is given. I hope your arm is steady. A little hartshorn-water or Eau de Cologne are excellent things to rub it with. I am sorry I never keep any of these things about me: Egypt cured me of them. Take Stewart the assistant-surgeon with you, and come back when the tulzie is over, and give me an account of it. You forget, major. I may never come back. And your opponent a Portuguese! Who is your second? Macdonald,—Macdonald of Inchkenneth. These pistols are very handsome, observed Ronald, with affected carelessness, as he examined the stones with which they were studded, and surveyed the flints and locks. Ah! they are indeed handsome. My grandfather took them out of the Duke of Douglas's belt, after he had unhorsed him at Shirramuir. They did some execution at Culloden, too.
- 44. On the right side, of course? Yes; in the army of the Prince. Use this one, with the cairn- gorum on the butt. The other throws high, and you would need to level to the boot to hit the belt. It happened so with me at Grand Cairo, when firing at a Turkish thief. I aimed at his sash, and the ball knocked off his turban. I would tell you all the story, but there is no time. I have no fear of you; so be off, my lad. God bless you! and steady your hand. Do not let it be said that a Portuguese gained and kept the ground before a Scotsman, and one of the Gordon Highlanders. At the gate of the Alcanzar he met Macdonald, and wrapping themselves up in their cloaks, as the morning air was cold and chilly, they hurried towards the bridge of Toledo. The streets appeared gloomy and dull in the grey light of the morning; and save their own foot-falls, no other sound broke the silence. The most public places were absolutely deserted. The shops under the piazzas of the Plaza, the stalls in the market-place, the cafés and tabernas were still all closed. Two or three halberdiers stood at the gate of El Medico's residence, and these were all they met, save a cloaked cavalier, who by a ladder of ropes suddenly descended from the window into the street, and disappeared. On reaching the bridge which spans the Tagus, immediately beneath the cannon and battlements of the city, they found Lisle and Chisholm awaiting them. A pistol-case lay on the parapet over which they were leaning, watching the smooth waters of the river as they hurried on between rocky ledges, banks overhung with foliage, and willow trees that flourished amidst the stream. A thick white mist was beginning to curl up from the bed of the river, exhaled by the
- 45. increasing heat of the morning sun, whose rays were tinging the east with red, and the cross on the beautiful spire of the cathedral, from one of the towers of which waved a broad and crimson banner, bearing the arms of Toledo—the imperial crown of Spain. A very disagreeable business this, Macdonald, whispered Chisholm, as he took the arm of the other, and led him aside to the parapet of the bridge, where they communed for a few seconds, leaving the principals, awkwardly enough, to stare at each other or admire the scenery, which ever they chose. Another attempt at an amicable arrangement was made, but without success; both parties were too much exasperated to yield in the least degree. Once more I ask you, Stuart, said Chisholm, coming forward, cannot this unhappy affair be adjusted without recourse to arms? You are a good-hearted fellow, Chisholm, and I fully appreciate your good intentions, but your words are lost upon me; I refer you to Mr. Lisle for an answer. Mine was the insult, and any apology should therefore come from him. It shall not! exclaimed Lisle bitterly; I will rather die than apologize. Stuart, you shall fight me; and if not— Lisle,—Lisle! your behaviour is very violent and most unjustifiable. I am the best judge, Mr. Macdonald. I fight in the cause of another, and not for myself, said Louis; and he turned haughtily on his heel, and again walked to the parapet. I am perfectly disposed to accept of an apology, observed Ronald to the seconds in a subdued voice; but as one will not be given, on Lisle's own head will rest the guilt of the blood shed this
- 46. morning. This quarrel has been of his own seeking, not mine. Heaven knows how loath I am to fight with him, but there is no alternative now. Measure the ground, and give us our weapons. Then, Macdonald, said Chisholm, all hopes of an accommodation are at an end? Quite: your principal is much to blame. But we must be expeditious,—see how red the horizon is; the drums will beat in ten minutes. During the measuring of the ground and the loading of the pistols, Ronald fixed his eyes on the saffron east, where the sun was about to rise in all its splendour above the mountains of Castile. Appearing black between him and the glowing sky rose the grassy height, crowned by the black old ruins of the castle of San Servan, that fortress so famous in romance, where Ruy, the Cid Campeador, was wont to spend the night in prayer and vigil. The sky was seen through its embrasured towers and empty windows, brightening in a blaze of glory all around, and giving promise of another day. Ronald gazed eastward wistfully. In ten minutes more the sun would be up, but by that time the eyes of either Lisle or himself might be sealed for ever. Ronald pictured what would be the emotions of Alice if her brother was slain, because she loved him well. He thought of his father, too; and remembered painfully that he would almost exult, if young Lisle was slain in this contest. His reverie was interrupted by Alister. All is ready,—Lisle has taken his ground, said he, putting into Ronald's hand the cold steel butt of the Highland pistol. For Heaven's sake, or rather for your own, appear a little more collected.
- 47. Lisle seems determined to shoot you, in revenge for your neglect of his sister. You have mentioned the only thing which can unnerve and unman me. Chisholm has told you, I suppose? Yes. An explanation might yet clear up this business. I scorn to ask it now! Are you ready? cried Chisholm, who had posted Lisle fourteen paces off. All ready. Stand aside, Macdonald. I believe that I must give the word. As you please. Alister retired, but, like Chisholm's, his heart was filled with a painful feeling of suspense and dread. The fatal word was given, and the report of both pistols instantaneously followed. Ronald fired into the air, but reeled backwards a few paces, and sunk on the road-way. Louis's stern look immediately relaxed, and he rushed towards him, tossing wildly away the other pistol. Heaven be merciful and look down on me, I have killed him! O Stuart, Ronald Stuart! speak to me, and he knelt over him with all the remorse that a brave and generous heart is capable of feeling, after the gust of passion has passed away. The ball has passed through his breast, whispered Macdonald in an agitated tone. Unclasp the plaid, and open his coat. There is no blood; it must be flowing internally. These observations, though made unintentionally, added greatly to the distress of Louis Lisle; but the unclasping of the shoulder-belt, the undoing of the sash, the plaid, and yellow riband of his gorget, aroused Ronald, who, to their great surprise, rose slowly to his feet.
- 48. Why, what are you all about, unharnessing me thus? I am not wounded, but I have received a devil of a shock. By a perfect miracle I have been saved. One I shall ever bless! said Lisle, pressing his hand. How is this? exclaimed Chisholm in astonishment; the ball has glanced off and torn your coat, as if you wore a corslet under it. By Jove! the miniature has saved him. He wears one: I used to quiz him about it at Merida, said Macdonald, as he pulled open the yellow lapel of the regimental coat, and displayed the little portrait hung around his neck by a chain. You perceive that the silver case has turned the ball, which has become flattened against the parapet yonder. Such a very narrow escape! The miniature! how comes this to pass? asked Lisle. Have you still preserved and worn it thus, notwithstanding your change of sentiments? Listen to me, Lisle. I vow to you by Heaven and my honour, that my sentiments are yet unchanged: they are the same as in that hour when I first received this miniature from your own hand; and from that time until this I have continually worn it near my heart, preserving it carefully and preciously as any monk does here the piece of wood which he considers a part of the true cross. Never yet have I parted with this relic for a moment, although I own that I was on the point of destroying it when I first received intimation of the intended alliance between the Earl of Hyndford and your sister, Miss Lisle,—an alliance probably formed by this time. The Earl of Hyndford! exclaimed Louis, in a tone of astonishment. Has that accursed and silly report been the cause of
- 49. our long alienation and quarrelling? Hyndford,—I had forgotten that affair altogether, or never supposed it could have reached you here in Spain. We have both been cruelly mistaken, but all will be happiness again. Give me your hand, Stuart, and we will be friends and brothers as of yore. Your heart is still unchanged, and I pledge you my honour that the affections of Alice are yours as much as ever. But this hostile meeting must be concealed from her, otherwise we should never be forgiven. Our seconds will never speak of the matter; their honour is a sufficient warrant for their secrecy. Further conversation, and the congratulations of Chisholm and Macdonald, were cut short by the drums beating, and they were all compelled to hurry off. Lisle took the arm of Ronald, and they went towards the muster-place by a different route from that pursued by their seconds, so that they might freely converse and give scope to their thoughts. A most agreeable revulsion of feeling had taken place in their minds. O Ronald Stuart! I have been much to blame in this business, said Lisle, much to blame indeed. And can you forgive me? Freely, Louis, replied the other, pressing his hand. I admire the spirit with which you have perilled life and limb for the cause of Alice. And so the dear girl is yet true? True as the sun! But I was infuriated,—almost maddened by your seeming indifference. It now flashes upon my mind that you mentioned Lord Hyndford in our unlucky quarrel at La Nava. Until this hour I had forgotten that; and probably but for our mountain pride and Scottish stubbornness, we might have come to a satisfactory explanation twelve months ago. What a deal of bitter feeling the paragraph of that wretched newspaper has occasioned!
- 50. But that is all at an end, and now, thank Heaven! we will no longer greet each other like hostile clansmen, with gloomy and averted eyes, as our sires did of yore. In all her letters to me Alice has deplored that for twelve months past you have broken off all correspondence with her,—indeed never having written once since you left Lochisla; and my excuses appear to have been very unsatisfactory to her. I feared that my letters might fall into Sir Allan's hands, and excite his displeasure. And afterwards our quarrel at La Nava appeared to confirm my suspicions— Say no more of them. I have in my possession a letter from her to you. I was intrusted with it on leaving home; but so great was the irritation I felt from our meeting at La Nava, that instead of delivering it, it has lain in my baggage until this hour,—nearly a whole year. Cruel and foolish! Ah, Lisle! how could you be so vindictive? Doubtless it would have unravelled this matter. You know not by what indignant sentiments I was prompted. Pride hardened my heart, for I loved Alice dearly; but, Stuart, I have heard some strange stories whispered at our mess-table, in which your name was entwined with that of a certain Donna Catalina. You change countenance. Poor Villa Franca; she was indeed a very beautiful woman, and I will acknowledge that, jealous and irritated as I was at Alice's supposed desertion, I yielded greatly to the charms of the noble Spanish lady; but I swear to you, Louis, that Alice—Alice alone, is the only being, the only woman I have ever truly loved! How much I
- 51. long to behold this letter, and read the words her white hand has traced, although so many months ago! Gentlemen, the regiment has fallen in, said the serjeant-major, breathlessly overtaking the loiterers. The adjutant sent me to look for you, Mr. Lisle. You are to carry the king's colour to-day, sir. They hurried off. Ronald derived the most exquisite pleasure from this reconciliation with his old friend; and it was alone equalled by the delightful idea that Alice yet loved him, and was the same gentle, winning, and blooming creature as ever,—and would yet be his, when all the perils of campaigning were past. Eagerly he longed for an opportunity to write: and what a deal he had to tell her,—of love and war, of future happiness, and mutual tenderness! The long-detained letter of Alice could not be procured from the depths of Lisle's baggage-trunks, until the halt at the ruinous little town of Villa Mayor. Although the march was only twelve miles, and lay along the left bank of the Tagus, among the most beautiful scenery,—wood and water, rocks and ruins, fields and vineyards,—it appeared to Ronald the longest and most wearisome he had ever performed. As soon as he received the letter from Louis, he rushed away to a secluded nook or bower of orange-trees, by the river side, and prepared to con it over in secret. He hastily kissed and broke the seal, which bore the crest of the Monteiths of Cairntowis, with the motto Keepe tryste. Ronald knew the signet ring of his mother, which he had given to Alice when he bade her adieu in the lawn before Inchavonhouse.
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