%Nr: DS-2001-03
%Author: Erik de Haas
%Title: Logics for OO Information Systems: a semantic study of object
% orientation from a categorial-substructural perspective.
Recent years have seen the convergence of many disciplines in
information systems facilitated by the concepts of Object
Orientation. Not least has been the convergence of the languages for
Object Oriented analysis and design, manifested in the definition of
the industrial standard UML (Unified Modeling Language [UML97],
[UML99]) for such languages. Moreover the integration of information
design languages into integral software development tools, enabling
automatic database (persistent) model generation and code generation,
indicate that these kinds of languages and concepts have grown to a
mature state.
The theme of this thesis is a semantical investigation in Object
Oriented (OO) modeling and database languages. The semantical
investigation strives to give a thorough mathematical description of
the concepts used in OO design and database languages. Such a
mathematical description gives an insight into the constructs used,
and can be used to develop and refine automatic development tools and
query optimalization techniques for computing with OO information
objects. Fact is, most object oriented design languages, and
especially UML, have no clear mathematical foundation. Nevertheless a
lot of 'formal' tasks like code generation and 'database modeling' are
performed in these languages. The resulting systems therefore are
suspect of ambiguities and inconsistencies, and hence sometimes valid
UML expressions cannot be processed. Research in the mathematical
foundations of OO concepts aims to aid the development of OO language
processing, by taking away the non-clarities and providing a formal
and consistent way of interpreting the language.
The semantical investigation in Object Oriented design languages is
especially interesting because the concepts of object orientation
originate from practice and were designed to help information analysts
and designers to accurately describe information models that re°ect
aspects of the real world. In this respect this research touches on
themes from philosophy, where it is an important goal to accurately
describe aspects of the real world.
In this thesis we will study the semantics of object oriented design
and database languages in detail. The thesis will provide a thorough
description of the concepts that can be expressed in UML and like
languages We will cover all the main concepts of object orientation
such as identity, inheritance, encapsulation etc.. Moreover, we will
study languages for specifying information systems from a more general
perspective and then identify the really basic concepts of talking
about information objects. In this exercise we will encounter serious
philosophical controversies that are inherent in talking about
objects, but often ignored in the information system practice. It
turns out that in the practice of information analysis, the
information modeler runs into hard philosophical problems in his
attempt to accurately describe the aspects of the real world he wants
to capture.
The major artifact we will present in this thesis is a language for
modeling information systems. This language contains all the main
concepts of object orientation. It is a generalization of the object
modeling part of UML (a fragment of the language constructs of UML,
present in several diagramming techniques of UML). The basic building
block of the language is a so called category and contains graphical
and textual components. We will do the necessary mathematics for this
language in order to obtain a formal semantics for the object oriented
concepts. We will develop a formal syntactic theory for the language
and provide a rigid mathematical model in which we will interpret the
language. In this setting we can give a clear semantics for the
basic language constructs of both object oriented modeling and design
languages and object oriented database and programming
languages. For the semantic study we will use the arsenal of modal and
substructural logic and categorial grammars. This branch of
mathematics is used heavily in the study of natural language and
computation theories and the study on the OO concepts contributes a
nice application of the theory with promising extensions for
intelligent information systems and data mining. Moreover, we can
identify the potential philosophical controversies associated with
describing aspects of the real world in the information analysis
practice. Such an identification will enable the information modeler
to choose a consistent interpretation of the models he writes down.
Several parts of this thesis have already been communicated to the
scientific community in various papers. A first version of the language
of categorial graphs appeared in [Haas95] and [Haas94]. Extensions on
this research in relation to natural language learning and data mining
were published in [HaasAdriaans99], [AdriaansHaas99] and
[AdriaansHaas00]. Preliminary research on object orientation and
information systems theory, which provided the inspiration to ex-
plore this interesting subject more thoroughly, appeared in
[HaasEmdeBoas93], [PomykalaHaas93], [PomykalaHaas94],
[PomykalaHaas96].
This thesis is structured as follows:
* Part1: General analysis of Object Oriented technology. Part 1
contains a general analysis of the concepts and intricacies of
object orientation in information systems. It is the
conceptualization of the domain of our semantical investigations.
- In Chapter 1 we will describe the information system analysis and
design practice. We will focus specifically on the object
oriented analysis and design practice and the related object
oriented database models. We will discuss the use of languages
for analysis and design and databases, and give an overview of the
languages used in practice (especially the industry standard
UML). We will see that this practice imposes requirements on the
language and its interpretation in the research context.
- In the second chapter, we present in detail the family of notions
and concepts for which we will do the semantic research. Note that
much debate is possible on the exact interpretation of information
system notions that originate from actual use. We will discuss the
notions for object oriented (new generation) information systems
in a critical way, and provide a motivation for the interpretation
we will use.
* Part 2: OO Modeling Proposal: Categorial Graphs. In this part we
propose a model in which we can research the object oriented
analysis and design practice.
- Chapter 3 will introduce a language for talking about information
systems. This is the syntactic domain in which we can denote
(graphically and textually) the concepts discussed in part 1. This
language is a generalization of the common OO information system
design languages. We will especially show its expressiveness by
comparing it to UML. In e®ect, the language presented will be a
formal syntactic theory for a generalized fragment of UML. The
language is built from a syntactic construct we call a
categorial graph (borrowing the term 'category' from Aristotle);
and the language therefore is called the language of categorial
graphs.
- Chapter 4 contains the semantics of the categorial graph language. We
will present an interpretation of the language that talks about object
oriented information systems. This interpretation will be a logic based
on the theory of modal and substructural logics.
* Part 3: Logical aspects. The chapters in this part present logical
aspects of the theory of object oriented information systems.
- In chapter 5 we will explain the benefits of formal semantics and
describe the approach and attitude to tackle the semantics for
information systems taken in this thesis. We will explain the
logical aspects of doing semantics, and also position this
research in the research field of logic, as it touches some very
interesting problems in current logic research.
In chapter 6 we will investigate the logic of categorial
graphs. We will discuss logical aspects, especially soundness,
completeness and the computational complexity of the logics for
categorial graphs.
* Part 4: Philosophical backgrounds. In this part we discuss
philosophical issues involved in information system modeling and
object oriented concepts.
- In Chapter 7 we take a little step back, and will formulate only
the basic concepts we like to have in our language that talks
about information systems. We will right away discover that this
basic list of desiderata already confronts us with hard problems
that are (still) very actual in philosophy.
* Part 5: Conclusion This part contains a wrap up of the themes we
discussed in this thesis.
In chapter 8 we summarize what we have done and evaluate what we
have achieved.