Preface
Information modelling and knowledge bases are becoming very important topics not only in academic communities related to information systems and computer science but also in the business field of information technology.
Currently, the structural complexity of information resources, the variety of abstraction levels of information, and the size of databases and knowledge bases are continuously growing. We are facing the complex problems of structuring, sharing, managing, searching and mining data and knowledge from a large amount of complex information resources existing in databases and knowledge bases. New methodologies in many areas of information modelling and knowledge bases are expected to provide sophisticated and reliable solutions to these problems.
The aim of this series of Information Modelling and Knowledge Bases is to provide research communities in information modelling and knowledge bases with scientific results and experiences achieved by using innovative methodologies in computer science and other disciplines related to linguistics, philosophy, and psychology.
Those interdisciplinary research results include common interests in understanding and solving problems on information modelling and knowledge bases, as well as applying those research results to the practical application areas.
The research topics in this series are mainly concentrated on a variety of themes in the important domains:
• theoretical and philosophical basis of concept modelling and conceptual modelling,
• conceptual modelling, information modelling and specification,
• conceptual models in intelligent activity,
• collections of data, knowledge, and descriptions of concepts,
• human-computer interaction and modelling,
• database and knowledge base systems,
• software engineering and modelling and
• applications for information modelling and knowledge bases.
It is very significant to recognize, study and share new areas related to information modelling and knowledge bases on which great attention is focused. Therefore, cognitive science, knowledge management, linguistics, philosophy, psychology, logic, and management science are relevant areas, too. This is reflected in the number of research results dealing with multimedia databases, WWW information managements, and temporal-spatial data models. These new directions are pushing the frontier of knowledge and creating novel ways of modelling real worlds.
To achieve these aims in this series, the international program committee has selected 16 full papers, 11 short papers and 1 position paper in a rigorous reviewing process from 38 submissions.
The selected papers cover many areas of information modelling, concept theories, database semantics, knowledge bases and systems, software engineering, WWW information managements, context-based information access spaces, ontological tech-
nology, image databases, temporal and spatial databases, document data managements, and many more.
In Program Committee, there were 32 well-known researchers from the areas of information modelling, concept theories, conceptual modelling, database theory, knowledge bases, information systems, linguistics, philosophy, logic, image processing, temporal and spatial databases, document data managements and other related fields. We are very grateful for their great work in reviewing the papers.
We hope that the series of Information Modelling and Knowledge Base will be productive and valuable in the advancement of research and practice of those academic areas.
The Editors
Yasushi Kiyoki
Jaak Henno
Hannu Jaakkola
Hannu Kangassalo
Program Committee
Co-Chairs:
Yasushi Kiyoki, Keio University, Japan
Hannu Kangassalo, University of Tampere, Finland
Members:
Alain Pirotte, University of Louvain, Belgium
Anneli Heimbürger, Tampere University of Technology, Pori, Finland
Arne Sølvberg, Norwegian University of Science and Technology, Norway
Benkt Wangler, Skövde University, Sweden
Bernhard Thalheim, Kiel University, Germany
Björn Nilsson, Astrakan Strategic Development, Sweden
Cristine Sernadas, Institute Superior Tecnico, Portugal
Eiji Kawaguchi, Keio University, Japan
Esteban Zimanyi, Universite Libre de Bruxelles (ULB), Belgium
Hannu Jaakkola, Tampere University of Technology, Pori, Finland
Isabelle Mirbel-Sanchez, Université de Nice Sophia Antipolis, France
Jeffery Xu Yu, Chinese University of Hong Kong, Honk Kong
Jörgen Fischer Nilsson, Denmark Technical University, Denmark
Koichi Nozaki, Nagasaki University, Japan
Manfred A. Jeusfeld, Tilburg University, The Netherlands
Marie Duží, Technical University of Ostrava, Czech Republic
Martti Juhola, University of Tampere, Finland
Michael Schrefl, University of Linz, Austria
Olga De Troyer, Vrije Universiteit Brussel, Belgium
Pierre-Jean Charrel, Université Toulouse 1, France
Seiji Ishikawa, Kyushu Institute of Technology, Japan
Takehiro Tokuda, Tokyo Institute of Technology, Japan
Tapio Niemi, University of Tampere, Finland
Veikko Rantala, University of Tampere, Finland
Xing Chen, Kanagawa Institute of Technology, Japan
Yoshihide Hosokawa, Nagoya Institute of Technology, Japan
Yoshihiro Okada, Kyushu University, Japan
Yukihiro Itoh, Shizuoka University, Japan
Yutaka Funyu, Iwate Prefectural University, Japan
Yuzuru Tanaka, University of Hokkaido, Japan
Organizing Committee
Jaak Henno, (Organizing Committee Co-Chair), Tallinn University of Technology, Estonia
Hannu Jaakkola, (Organizing Committee Co-Chair), Tampere University of Technology, Pori, Finland
Hannu Kangassalo, University of Tampere, Finland
Eiji Kawaguchi, Keio University, Japan
Yasushi Kiyoki, Keio University, Japan
Ulla Nevanranta (Publication), Tampere University of Technology, Pori, Finland
Yurika Suzuki (Publication), Keio University, Japan
Permanent Steering Committee
Hannu Jaakkola, Tampere University of Technology, Pori, Finland
Hannu Kangassalo, University of Tampere, Finland
Eiji Kawaguchi, Keio University, Japan
Setsuo Ohsuga, Japan (Honorary member)
Additional
Reviewers
Hideki Noda, Kyushu Institute of Technology, Japan
Jun Sasaki, Iwate Prefectural University, Japan
Mina Akaishi, University of Tokyo, Japan
Mitsuhisa Taguchi, Tokyo Institute of Technology, Japan
Paula Gouveia, Instituto Superior Tecnico, Portugal
Per Backlund, University of Skövde, Sweden
Satoru Kogure, Shizuoka University, Japan
Sven Casteleyn, Vrije Universiteit Brussel, Belgium
Tae Yoneda, Iwate Prefectural University, Japan
Tetsuya Suzuki, Tokyo Institute of Technology, Japan
Wesley Bille, Vrije Universiteit Brussel, Belgium
Zhao Peixiang, Chinese University of Hong Kong, Hong Kong
Preface v
Yasushi Kiyoki, Jaak Henno, Hannu Jaakkola and Hannu Kangassalo
Committees vii
Additional Reviewers viii
A Model for Describing and Annotating Documents
Nicolas Dessaigne and José Martinez
Web Ontology Languages: Theory and Practice – Will They Ever Meet?
Marie Dužíand Anneli Heimbürger
Object Order Based on Concept Analysis and Moebius Inversion Function
Petr Gajdoš and Daniela Ďuráková
A Semantic Spectrum Analyzer for Realizing Semantic Learning in a Semantic Associative Search Space
Yasushi Kiyoki, Xing Chen and Hidehiro Ohashi
Theory and Implementation on Automatic Adaptive Metadata Generation for Image Retrieval
Hideyasu Sasaki and Yasushi Kiyoki
A Meme Media Framework for Introducing a Multimodal User Interface to Existing Web Applications
Kimihito Ito
Privacy Enhanced Information Systems
Sabah S. Al-Fedaghi, Gunar Fiedler and Bernhard Thalheim
Description Logics, Data Modelling and Relational Dependencies
Tapio Niemi, Marko Niinimäki and Santtu Toivonen
Modelling, Searching and Utilising Grid Resources and Services
Marko Niinimäki, Santtu Toivonen and Tapio Niemi
Conceptual Modelling (and Problem Solving Techniques) for Complex Narrative Events
Gian Piero Zarri
Role of Models in Knowledge Transfer During OO Software Development
Oksana Nikiforova, Marite Kirikova and Wita Wojtkowski
1
20
38
50
68
83
94
112
127
138
156
Toward a Cooperative Recognition of Human Behaviors and Related Objects 172
Tadahiro Kitahashi, Atsuhiro Kojima, Mirai Higuchi and Kunio Fukunaga
A Reliable and Useful Information Distribution System: The “Kuchicomi Network”
Jun Sasaki, Tae Yoneda and Yutaka Funyu
180
Object-Oriented Model for Fire Spread Prediction
Guillermina Pertino, Sabrina Tocho, Arturo Zambrano and Silvia Gordillo
191
Knowledge Entry Maps: Structuring of Method Knowledge in the IT Industry 205
Remko Helms, Sjaak Brinkkemper, Job van Oosterum and Frank de Nijs
Building a Conceptual Skeleton for Enterprise Architecture Specifications 219
Veikko Halttunen, Antti Lehtinen and Riku Nykänen
Fixed-Point Quantifiers in Higher Order Logics 237
Klaus-Dieter Schewe and José María Turull Torres
Discovery of Narrativity on the WWW Based on Perspective Information Access
Mina Akaishi, Nicolas Spyratos, Koichi Hori and Yuzuru Tanaka
A Computer Science Text Corpus/Search Engine X-Tec and Its Applications
Takehiro Tokuda, Yusuke Soyama and Tetsuya Suzuki
Deriving Semantic from Images Based on the Edge Information 260 Xing Chen, Tony Delvecchio and Vincenzo Di Lecce
Evolving the Database Co-Design Framework by SPICE
Hannu Jaakkola, Timo Mäkinen, Bernhard Thalheim and Timo Varkoi
Reconstructing Geons in Database Semantics
Roland Hausser
Query Optimisation as Part of Distribution Design for Complex Value
Hui Ma and Klaus-Dieter Schewe
Position Paper: Digital Media Archive for Academic Resources
Takanari Hayama, Eiji Kawaguchi and Yasushi Kiyoki
An Ontology Learning and Reasoning Framework
Hele-Mai Haav
Strong Relevant Logic as the Universal Basis of Various Applied Logics for Knowledge Representation and Reasoning
Jingde Cheng
Concept Theory in the Context of Information Systems
Jari Palomäki and Momir Radičević Describing Knowledge
Enn Tyugu
Y. Kiyoki et al. (Eds.)
IOS Press, 2006
© 2006 The authors. All rights reserved.
N.DessaigneandJ.Martinez/AModelforDescribingandAnnotatingDocuments
N.DessaigneandJ.Martinez/AModelforDescribingandAnnotatingDocuments
Information Modelling and Knowledge Bases XVII Y. Kiyoki et al. (Eds.) IOS Press, 2006 © 2006 The authors. All rights reserved.
Web Ontology Languages:
theory and practice – will they ever meet?
Marie DUŽÍ* and Anneli HEIMBÜRGER**
*VSB-Technical University of Ostrava 17. listopadu 15, 708 33 Ostrava, Czech Republic marie.duzi@vsb.cz
**Tampere University of Technology, Pori, Advanced Multimedia Center P.O. Box 300, FIN – 28101 Pori, Finland anneli.heimburger@tut.fi
Abstract. The current state of Semantic Web ontology languages is briefly described, and the ontology languages are characterised from the logical point of view. Generally, these languages are based on the first-order predicate logic enriched with ad hoc higher-order constructs wherever needed. We argue that in the Semantic Web we need a rich language with transparent semantics, in order to build up metadata on the conceptual level of the Semantic Web architecture. A powerful logical tool of Transparent Intensional Logic (TIL) is described, which provides a logico-semantic framework for a fine-grained knowledge representation and conceptual analysis. TIL is based on a rich ontology of entities organised in an infinite ramified hierarchy of types. The conceptual role of TIL in building ontologies is described, and we show that such a system can serve as a unifying logical framework. Concluding we argue that the conceptual and logical level of the Web architecture have an important role, and we should pay a due attention to these levels.
Keywords. Ontology languages, Semantic Web, Transparent Intentional Logic (TIL), hierarchy of types, concepts, structured meanings, XML Linking Language (XLink), Resource Description Framework (Schema), RDF, RDFS, Ontology Web Language (OWL), SKIF (Knowledge Interchange Format), Description Logic
1. Introduction
The Web was proposed as a tool for representing relationships between named objects, drawing together knowledge from scattered systems into a common framework [2]. The main aim of the Semantic Web initiative is to develop the current Web towards the original proposal. W3C’s Semantic Web Activity develops standards and technologies, which are designed to help machines to understand more information on the Web [14, 29]. The word “semantic” in the context of Semantic Web means “machine-processible” [4]. The main idea is of having the data on the Web defined and linked in such a way that it can be used for more effective information retrieval, knowledge discovery, automation, integration and reuse of information across various applications, organisations and communities. To meet these goals, the World Wide Web Consortium (W3C) has defined a layer model for the Semantic Web (Figure 1), and knowledge representation and ontology languages are being developed. The Semantic Web is vitally dependent on a formal meaning assigned to the constructs of its languages. For Semantic Web languages to work well together their formal meanings must employ a common view (or thesis) of representation [15], otherwise it will not be possible to reconcile documents written in
different languages. A common underpinning is especially important for the Semantic Web because it is envisioned to contain several languages, as in Tim Berners-Lee's “layer cake” diagram (Figure 1) first presented at XML 2000 [3]. The diagram depicts a Semantic Web Architecture in which languages of increasing power are layered one on top of the other. Unfortunately, the relationships between adjacent layers are not specified, either with respect to the syntax or semantics. Naturally but unfortunately, the model isbeing gradually realised in a bottom up way; languages in particular layers come into being in an ad hoc way, without a deep logical insight. Thus the languages often lack an exact semantics and ontological definitions of particular entities; in the syntactic constructs, particular abstract levels are mixed together.
Trust level
Digital signature, annotation
Logical and inference level
Rule-based systems, ML, …
Ontology level
OWL, WordNet, RosettaNet, …
Metadata level
RDF, RDFS, …
Structure level
XML, XLink, XML Schema, …
Internet level
Unicode, URI, …
The notion ‘ontology’ is understood in many distinct ways: formalisation, conceptual analysis, hierarchical classification, conceptualisation, etc. We are going to show that ‘ontology’ can be understood as a conceptual analysis of a given universe of discourse, i.e., of what (which entities) we talk about, and how, by means of which concepts we capture these entities. Logical forms (constructions) rendering the basic stock of explicit knowledge serve as the base, from which logical consequences can be derived by an inference machine so that to obtain the inferable stock of knowledge [8]. The more fine-grained the analysis is, the more accurate inferences the machine can perform. In an ideal case, the inference machine should be able to derive just thelogical consequences of the base: it should not over-infer (derive something that does not follow), nor under-infer (not to derive something that does follow). We show that the current state-of-arts is far from being ideal. Web ontology languages are based on the 1st-order predicate logic (FOL). Though FOL has become stenography of mathematics, it is not expressive enough when used at the natural language area. The obvious disadvantage of the FOL approach is that treating higher-order properties and relations like individuals conceals the ontological structure of the universe, and knowledge representation is not comprehensive. Moreover, when representing knowledge, inference paradoxes are inevitable. Thus for applications where even the full power of FOL is not adequate, it would be natural to extend the framework to a higherorder logic (HOL). A general objection against using HOL logic is its computational intractability. However, HOL formulas are relatively well understood, and reasoning systems for HOLs do already exist, e.g., HOL [11] and Isabelle [25]. Though the Web languages have been enriched by a few constructs exceeding the power of FOL, these additional constructs are usually not well defined and understood. Moreover, particular
Figure 1: Semantic Web architecture
languages are neither syntactically nor semantically compatible. The W3C efforts at standardization resulted in accepting the Resource Description Framework (RDF) language as the Web recommendation. However, this situation is far from satisfactory. Quoting from Horrocks and Schneider [15]: “The thesis of representation underlying RDF and RDFS is particularly troublesome in this regard, as it has several unusual aspects, both semantic and syntactic. A more-standard thesis of representation would result in the ability to reuse existing results and tools in the Semantic Web.”
In the paper we describe a powerful logical tool of transparent intensional logic (TIL), which provides a logico-semantic framework for a fine-grained knowledge representation and conceptual analysis. TIL is based on a rich ontology of entities organised in an infinite ramified hierarchy of types. The language of TIL constructions (hyperintensionally individuated meanings) can serve as an ideal knowledge representation and query language. A common objection against such a rich system, namely that it is too complicated and computationally intractable, is in our opinion rather irrelevant: formal knowledge specification in TIL is semantically transparent and comprehensible, with all the semantically salient features explicitly present. In the Semantic Web we need such a highly expressive language so that to first know what is there, and only afterwards to try deriving the consequences. The fact that for higher-order logics such as TIL there is no semantically complete proof-system is not important. Only when understanding the problem and knowing “what is there”, we can try to solve the problem and derive consequences. Moreover, the TILframework mightat least serve as a both semantic and terminological standard for the development of new languages, as an ideal to which we should aim at.
The paper is organised as follows. First, in chapter 2 we recapitulate the current state of Web ontology languages from two viewpoints. In paragraph 2.1 Web ontology languages are described from the inter-relations point of view and in paragraph 2.2 from the logical point of view. We show here that the Web ontology languages are mostly based on the first-order predicate logic approach. In Chapter 3, an expressive system of the Transparent Intensional Logic (TIL) is described. After an informal introduction we provide particular definitions, describe the method of semantic analysis and characterise important conceptual relations. Finally, in Chapter 4, the conceptual and terminological role of TIL in building ontologies is described.
2. Web Ontology Languages
The lowest levels of the Semantic Web are based on mark-up languages. By means of schemas and ontology classifications, types of resources and types of inter-relationships between the resources can be specified. At the bottom level, the Unicode and URI layers make sure that international character sets are used and provide means for identifying the resources in the Semantic Web. At the very core level of the Web, there is the XML layer with linking, style and transformation, namespace and schema definitions, which forms the basis for the Semantic Web definitions. On the metadata level we can find RDF and RDF Schema for describing resources with URI addresses and for defining vocabularies that can be referred to by URI addresses, respectively. The ontology level supports the evolution of a shared semantic specification and conceptualization of different application domains. The ontology level is based on the OWL recommended by W3C, which is based on the 1st-order Description logic framework. Based on common logic, the SKIF language accommodates some higher-order constructs. At the logical level, simple inferences based on ontologies can be drawn. As far as we know, the only ontology language supporting inferences at this level is a Semantic Web Rule Language (SWRL) combining OWL and RuleML [16]. At the highest level, the focus is on trust, i.e., how to guarantee the reliability of the data obtained from the Web. Currently, a common research project CoLogNet II (Network of
Excellence in Computational Logic II) of fourteen European universities, lead by the Free University of Bozen-Bolzano, Italy, is prepared. The goal of this project can be characterised as the development of a powerful Web-inference machine based on a highly expressive logical semantics.
2.1 Web Ontology Languages from Inter-relating Point of View
XML Linking Language (XLink, [32]) is a W3C recommendation which allows elements to be inserted into XML documents in order to create and describe relationships between and inside Web resources XLink uses XML syntax [30]to create linking and navigation structures. XPointer language [31] is used to identify regions in XML documents. XLink supports simple, unidirectional, unary and untyped links as well as more sophisticated, extended links. Extended links can be bidirectional and n-ary. Arcs are used to describe traversal rules in an n-ary link. XLink also defines a linkbase.xml for storing a set of extended links to separate XML file. Extended links can also have attributes.XLink consists of three attribute categories: semantic, behaviour and traversal attributes. XLink’s attribute space is flexible and can be extended in order to create for example time-sensitive linking structures, which represent context-based inter-relations and low level way of inferring [13]. XLink is at the moment the only formal linking language which is based on an international standard [17].
The Resource Description Framework (RDF) was designed to provide a common way to describe information in a way that it can be read and understood by computer applications [34]. The data model of the RDF includes three basic elements. Resources are anything with an URI address. Properties specify attributes and/or (binary) relations between resources and an object used to describe resources.Statements of the form ‘subject, predicate, object’associate a resource and a specific value of its property.Both XLink and RDF provide a way of creating relations between resources. However, RDF as a metadata specification is designed for describing the contents of resources and their relations as graphs, while XLink is designed for specifying and traversing hyperlinks. From XLink’s point of view RDF can have two roles: harvesting RDF statements from XLinks [27] and meta-information description of XLink structures. An example of an RDF graph description of an extended link is illustrated in Figure 2.
As RDF describes resources with classes, properties and values, by means of RDF Schema (RDFS) an extension of RDF application-specific classes and properties can be defined [35]. RDF Schema doesn’t provide actual application-specific classes and properties; instead it provides a way of defining those. By means of RDFS it is possible to create simple vocabularies of a certain application domain, for example in technical documentation. In the Web environment vocabularies allow search engines, agents, authors and users to communicate.
In addition to XLink and RDF(S) another important facility to organize Internet resources are XML Topic Maps [24]. With topic maps an associative information structure, which is located outside that information can be created. A topic map usually contains several overlapping levels, which are semantically cross-linked. The core of the XML Topic Maps (XTM) 1.0 specification is formed of topics, which represent the subjects the topic map is about. Topics can be grouped in classes called topic types. A topic type is a category to which one given topic instance belongs. A topic may be linked to one or more information resources that are relevant to the topic in some way. Such resources are called occurrences of the topic. Occurrences are information resources relevant to a topic. Topics can be related through some association expressing given semantics. Just as topic and occurrences can be grouped according to type so can also associations between topics be grouped according to their types.
xlink:extended
xlink:typ
e
link1
xlink:href
An example of an extended link
xlink:title
link2
xlink:locato
xlink:locator
r
xlink:arc
xlink:from
xlink:actuate
xlink:onLoad
xlink:href
xlink:to
xlink:show
xlink:new
Figure 2: An example of an RDF graph
Each topic that participates in an association plays a role in that association called the association role. The topic map specification provides a language to represent knowledge, in particular the conceptual knowledge with which one distinguishes information resources semantically. The ontological engineering discipline applied to building topic maps focuses precisely on this aspect. Ontological engineering emphasizes careful conceptual design and construction of topic maps to reflect correctly the semantics of the underlying knowledge. The design and construction of topic maps that provide meaningful expression of knowledge should be based on established principles of ontological engineering.
According to the OWL (Web Ontology Language) overview [33], OWL is intended to be used when information contained in documents needs to be processed by applications, as opposed to situations where the contents only need to be presented to humans. OWL can be used to represent the meaning of terms in vocabularies and relationships between those terms. OWL has been designed on the top of XML, XLink, RDF and RDFS in order to provide more facilities for expressing meaning and semantics to represent machine interpretable content on the Web.
When thinking in wider sense, XML/XLink, RDF, RDFS and OWL can all be regarded as ontology languages in different levels as far as creating and describing interrelations and navigational structures between and inside XML documents are concerned. XML/XLink is the very basis for defining links and traversal rules between Web resources. However, it also contains a rich and extendable attribute space for describing semantic, behavioural and traversal characteristics of links. RDF provides means for describing metainformation on linking and navigational structures. RDFS defines a framework to describe vocabularies which can be applied to represent linkbases. By means of OWL like languages a vocabulary of terms and some specification of meaning between the terms can be specified. From thelinking point of view the Semantic Web isstill a network of linked nodes with different granularity levels of inter-relations, and itcan be considered from three different perspectives [19]: (a) universal library to be accessed and used by humans in a variety of information use contexts, (b) the backdrop work of computational agents carrying out activities on behalf of humans, and (c) a method for integrating knowledge bases and databases to perform tasks for humans. Current Web ontology languages are, however, far from meeting these points, in particular points (b) and (c), for their expressive power does not enable computational agents to involve an adequate inference machine.
2.2 Web Ontology Languages from the Logical Point of View
According to Horrocks and Patel-Schneider [15] building ontologies consists in a hierarchical description of important concepts in a domain, along with descriptions of properties of the instances of each concept and relations between them. Current ontological languages correspond roughly in their expressive power to the first-order predicate logic (FOL), with some higher-order ad hoc extensions. None of them (except of languages based on the Description logic framework) makes it possible to express modalities (what is necessary and what is contingent, i.e., which concepts are analytical and which empirical) and higher-order concepts. Concepts of n-ary relations are unreasonably modelled by properties. True, each n-ary relation can be expressed by n unary relations (properties): for instance the fact that G.W. Bush attacked Iraq can be modelled by two facts, namely that G.W. Bush has the property of attacking Iraq, and Iraq has the property of being attacked by G.W. Bush, but such a representation is neither comprehensive nor optimal.
The basis of a particular way of providing meaning for metadata is embodied in the model theory for RDF. RDF has unusual aspects that make its use as the foundation of representation in the Semantic Web difficult at best. In particular, RDF has a very limited collection of syntactic constructs, and these are treated in a very uniform manner in the semantics of RDF. The RDF thesis requires that no other syntactic constructs than the RDF triples are to be used and that the uniform semantic treatment of syntactic constructs cannot be changed only augmented [15]. In RDFS we can specify classes and properties of individuals, constraints on properties, and the relation of subsumption (subclass, subproperty). It is not possible, for instance, to specify properties of properties, e.g., that the relation (property) is functional or transitive. Neither it is possible to define classes by means of properties of individuals that belong to the class.
A recognition of the limitations of RDFS led to the development of new Web ontology languages such as OIL, DAML-ONT and DAML+OIL [28, 36]. These are used as the basis of a new W3C Web ontology language called the OWL. As a second language for the Semantic Web, OWL has been developed as an extension of RDFS. OWL (like DAML+OIL) uses the same syntax as RDF (and RDFS) to represent ontologies, the two languages are syntactically compatible. However, the semantic layering of the two languages is more problematical. The difficulty stems from the fact that OWL (like DAML+OIL) is largely based on the Description Logic [1], the semantics of which would normally be given by a classical first-order model theory in which individuals are interpreted as elements of some domain (a set), classes are interpreted as subsets of the domain and properties are interpreted as binary relations on the domain. The semantics of RDFS, on the other hand, are given by a non-standard model theory, where individuals, classes and properties are all elements in the domain. Properties are further interpreted as having extensions which are binary relations on the domain, and class extensions are only implicitly defined by the extension of the rdf:type property. Moreover, RDFS supports reflection on its own syntax: interpretation of classes and properties can be extended by statements in the language. Thus language layering is much more complex, because different layers subscribe to these two different approaches.
The third group of ontology languages lies somewhere between the FOL framework and RDFS. The group of relatively new languages include SKIF and Common Logic [12]. The SKIF syntax is compatible with functional language LISP, but in principle it is an FOL syntax. These languages have like RDFS a non standard model theory, with predicates being interpreted as individuals, i.e., elements of a domain. Classes are however treated as subsets of the domain, and their redefinition in the language syntax is not allowed.
Hence from the logicalpoint of view, the ontological languages can be divided into three groups: the FOL approach, the SKIF approach, and the RDF approach.
The FOL approach (DAML+OIL, OWL) is closely connected to the rather expressive Description Logic (DL): Languages of this group talk about individuals that are elements of a domain. The individuals are members of subclasses of the domain, and can be related to other individuals (or data values) by means of properties (n-ary relations are called properties in Web ontologies, for they are decomposed into n properties). The universe of discourse is divided into two disjoint sorts: the object domain of individuals and the data value domain of numbers. Thus the interpretation function assigns elements of the object domain to individual constants, elements of data value domain to value constants, and subclasses of the data domain to data types. Further, object and data predicates (of properties) are distinguished, the former being interpreted as a subset of the Cartesian product of object domain, the latter a subset of the Cartesian product of value domain. DL is rather rich, though being an FOL language. It makes it possible to distinguish intensional knowledge (knowledge on the analytically necessary relations between concepts) and extensional knowledge (of contingent facts).
The knowledge base of DL is thus divided into the so-called T-boxes (according to terminology or taxonomy) and A-boxes (according to contingent attributes of objects). Tbox contains verbal definitions, i.e., a new concept is defined composing known concepts. For instance, a woman can be defined: WOMAN = PERSON & SEX-FEMALE, and a mother: MOTHER = WOMAN & child(HASCHILDchild). Thus the fact that, e.g., mother is a woman is analytical (necessary) true. In the T-box there are also specifications of necessary properties of concepts and relations between concepts:the property satisfiability corresponding to a nonempty concept, the relation of subsumption (intensionally contained concepts), equivalence and disjointness (incompatibility). Thus, e.g., that a bachelor is not married is analytically (necessarily) true proposition. On the other hand, the fact that, e.g., Mr. Jones is a bachelor is a contingent unnecessary fact. Such contingent properties (attributes) of objects are recorded in A-boxes.
The SKIF approach: SKIF languages are syntactically compatible with LISP, i.e., the FOL syntax is extended with the possibility to mention properties and use variables ranging over properties. For instance, we can specify that John and Peter have a common property: p p(John) & p(Peter). The property they have in common can be, e.g., that they both love their wives. We can also specify that the property P is true of John, and the P has the property Q: P(John) & Q(P). If P is being honest and Q is being eligible, the sentence can be read as that John is honest, which is eligible. The interpretation structure is a triple <D, ext, V>, where D is the universe, V is the function that maps predicates, variables and constants to the elements of D, and ext is the function that maps D into sets of n-tuples of elements of D. SKIF does not reduce the arity of predicates.
The RDF approach: These languages originally did not have a model theoretic semantics, which led to many discrepancies. The RDF syntax consists of the so-called triples (subject, predicate and object), where only binary predicates are allowed. This causes serious problems concerning compatibility with more expressive languages. RDF(S) has become a Web ontological recommendation defined by W3C, and its usage is world spread. The question is whether it is a good decision. A classical FOL approach would be better, or even its standard extension to HOL would be more suitable for ontologies. Formalisation in HOL is much more natural and comprehensive, the universe of discourse is not a flat set of ‘individuals’, but properties and relations can be naturally talked about as well, which is much more apt for representation of ontologies.
Ontologies will play a pivotal role in the Semantic Web by providing a source of shared and precisely defined concepts of entities that can be used in metadata. The degree of formality employed in capturing these concepts can be quite variable, ranging from natural language to logical formalisms, but increased formality and regularity clearly facilitates machine understanding. We argue that conceptual formalisation should be
meaning driven, based on natural language. Formal language of FOL is not a natural language; it is a language of non interpreted formulas that enable us to talk about individuals, expressing their properties and relations between individuals, but not to talk about properties of (individuals, properties, functions, relations, properties of concepts, generally of higher-order objects), unless they are simple members of the universe. Thus inference machine based on FOL can under-infer, or paradoxically over-infer.
Here is an example: The office of the President of USA is certainly not an individual. It can be hold by individuals, but the holder and the office are two completely distinct things. The office (Church’s individual concept) necessarily has some requisites (like being occupied by at most one individual), which no its occupant has. In FOL, however, we have to treat the office as an individual. The paradoxes like the following arise:
The President of USA knows that John Kerry wanted to become the President of USA.
George W. Bush is the President of USA. Hence: George W. Bush knows that John Kerry wanted to become George W. Bush. Analysing (as it should be) ‘is’ in the second premise as the identity of individuals, we obtain the obviously non-valid conclusion. True, this shortcoming is usually overcome in FOL approach by introducing a special binary predicate ‘holds’. The second premise would then be translated into: (individual) George W. Bush holds (another individual) the President of USA. But then the inference machine under-infers, because it would not be possible to infer a valid consequence of the above premises, namely that George W. Bush knows that John Kerry wanted to become the President of USA.
Another shortcoming of FOL approach is the impossibility to handle (contingently) ‘non-denoting terms’ like the President of Czech Republic in January 2003, or the King of USA. In other words, translating the sentence that the King of USA does not exist into an FOL language, we obtain a paradox of existence (that being an individual, it exists, but actually it does not exist): x (x = k(USA)), but from (x = k(USA)) by existential generalisation we immediately derive that x (x = k(USA)).
A theory formalising reasoning of intelligent agents has to be able to talk about the objects of agents’ attitudes, to quantify over them, to express iterated attitudes and/or selfreferential statements, like agent a knows that an agent b knows that (he) believes that P, which in FOL leads to inconsistencies. Such theories have also to enable us to express the distinction between analytical and empirical concepts (what is necessary and what is just contingent), to express empty concepts, to talk about concepts and, last but not least, to express n-ary relations-in-intension between any entities (not only individuals) of our ontology. While this is beyond the expressive power of FOL, many richer logical systems with non-standard operators are proposed: modal, epistemic, intensional, temporal, nonmonotonic, paraconsistent, etc. These logics can be characterized as theories with ‘syntactically driven axiomatization’. They provide ad hoc axioms andrules that define a set of models, each logic partly solving particular kind of problems. Ontology language should be, however, universal, highly expressive, with transparent semantics and meaning driven axiomatisation. We have such a system at hand: the system of transparent intensional logic (TIL).
3. Transparent Intensional Logic (TIL)
3.1 TIL Informal Exposition: Hierarchy of Types
TIL is a logic that does not use any non standard operators; in this sense it is classical. However, its expressive power is very high; formalisation of meaning is comprehensive, with transparent semantics, closed to natural language. Notation is an adjusted objectual
version of Church’s typed -calculus, where all the semantically salient features are explicitly present. The two-dimensional ontology of entities we can talk about is in TIL organised in a ramified hierarchy of types. This enables us to logically handle structured meanings as higher-order, hyper-intensional abstract objects, thus avoiding inconsistency problems stemming from the need to mention these objects within the theory itself. Hyperintensionally individuated structured meanings are procedures, structured from the algorithmic point of view. Due to typing, any object of any order can be not only used, but also mentioned within the theory without giving rise to inconsistency.
On the ground level of the type-hierarchy, there are entities unstructured from the algorithmic point of view belonging to a type of order 1. Given a so-called epistemic base of atomic types( -truth values, -individuals, -time points, -possible worlds), mereological complexity is increased by an induction rule of forming partial functions: where , 1,…, n are types of order 1, the set of partial mappings from 1 … n to , denoted ( 1… n), is a type of order 1 as well.
TIL is an open-ended system. The above epistemic base { , , , } was chosen, because it is apt for natural-language analysis, but in the case of mathematics a (partially) distinct base would be appropriate; for instance, the base consisting of natural numbers, of type , and truth-values. Derived types would then be defined over { , }.
A collection of constructions that construct entities of order 1, denoted by *1, serves as a base for the induction rule: any collection of partial functions ( 1… n) involving *1 in their domain or range is a type of order 2. Constructions belonging to a type *2 that identify entities of order 1 or 2, and partial functions involving such constructions, belong to a type of order 3. And so on, ad infinitum.
3.2 TIL Informal Exposition: Constructions
Constructions are structured from the algorithmic point of view; they are procedures, or abstract algorithms, specifying how to arrive at less-structured entities. Since constructions are abstract, extra-linguistic entities, they are reachable only via a verbal definition. The ‘language of constructions’ is a modified version of the typed -calculus, where Montaguelike -terms denote, not the functions constructed, but the constructions themselves. The modification is extensive. Church’s -terms form part of his simple type theory, whereas our -terms belong to a ramified type theory [26].
Constructions qua procedures operate on input objects (of any type, even higher-order constructions) and yield as output objects of any type. One should not conflate using constructions as constituents of composed constructions and mentioning constructions that enter as input objects into composed constructions, so we have to strictly distinguish between using and mentioning constructions The latter is, in principle, achieved by using atomic constructions. A construction is atomic if it is a procedure that does not contain as a constituent any other construction but itself. There are two atomic constructions that supply objects (of any type) on which complex constructions operate: variables and trivialisations. Variables are constructions that construct an object dependently on valuation: they vconstruct. Variables can range over any type. If c is a variable ranging over constructions of order 1 (type *1), then c belongs to *2, the type of order 3, and constructs a construction of order 1 belonging to *1: the type of order 2. When X is an object of any type, the trivialisation of X, denoted 0X, constructs X without the mediation of any other construction. 0X is the atomic concept of X: it is the primitive, non-perspectival mode of presentation of X.
There are two compound constructions, which consist of other constituents: composition and closure. Composition is the procedure of applying a function f to an argument A, i.e., the instruction to apply f to A to obtain the value (if any) of f at A. Closure
is the procedure of constructing a function by abstracting over variables, i.e., the instruction to do so. Finally, higher-order constructions can be used twice over as constituents of composed constructions. This is achieved by a fifth construction called double execution
3.3 TIL Definitions
Definition 1 (Construction)
i)
ii)
iii)
Variablesx, y, z, … construct objects of the respective types dependently on valuations v;they v-construct.
Trivialisation: Where X is an object whatsoever (an extension, an intension or a construction), 0X constructs X.
Closure: If x1, x2, …,xn are pairwise distinct variables that v-construct entities of types 1, 2, …, n, respectively, and Y is a construction that v-constructs an entity of type , then [ x1…xn Y] is a construction called closure, which v-constructs a function of type ( 1… n) mapping 1 … n to .
iv) Composition: If X v-constructs a function f of a type ( 1… n), and Y1,…,Yn vconstruct entities A1, …, An of types 1,…, n, respectively, then the composition [X Y1 … Yn] v-constructs the value (an entity, if any, of type ) of the (partial) function f on the argument A1, …, An . Otherwise the composition [X Y1 … Yn] does not v-construct anything: it is v-improper.
v) Double execution: If X is a construction of order n, n 2, that v-constructs a construction X’ (of order n–1), then 2X v-constructs the entity v-constructed by X’. Otherwise the double execution 2X is v-improper.
vi)Nothing is a construction, unless it so follows from i) through v).
Definition 2 (Ramified hierarchy)
Let B be a base, i.e. a collection of pair-wise disjoint, non-empty sets.
T1 (types of order 1)
i)Every member of B is an elementary type of order 1 over B.
ii)Let , 1, ..., m (m > 0) be types of order 1 over B. Then the collection ( 1 ... m) of all m-ary (total and partial) mappings from 1 ... n into is a functional type of order 1 over B.
iii)Nothing is a type of order 1 over B unless it so follows from T1 i) ii).
Cn (constructions of order n over B)
i)Let x be a variable ranging over a type of order n. Then x is a construction of order n.
ii)Let X be a member of a type of order n. Then 0X, 2X are constructions of order n.
iii)Let X, X1,...,Xm (m > 0) be constructions of order n over B. Then [X X1...Xm] is a construction of order n.
iv)Let x1,...xm, X (m > 0) be constructions of order n over B. Then [ x1...xm X] is a construction of order n.
v)Nothing is a construction of order n over B unless it so follows from Cn i) v).
Tn+1 (types of order n + 1)
Let n be the collection of all construction of order n over B
i) n and every type of order n are types of order n + 1.
ii)If m > 0, and , 1,..., m are types of order n + 1 over B, then ( 1 m) (see T1 ii)) is a type of order n + 1 over B.
ii)Nothing is a type of order n + 1 over B unless it so follows from Tn+1 i) ii).
Notational conventions An object A of the type is called an -object, denoted A/ . That a construction C constructs an -object will be denotedC . We use infix notation
without trivialisation for truth-value connectives (conjunction), (disjunction), (implication), for an identity sign = and for binary number relations , <, >, Examples (a) The function +, defined on natural numbers (of type ), is not a construction. It is a mapping of type ( ), i.e., a set of triples, the first two members of which are natural numbers, while the third member is their sum. The simplest construction of this mapping is 0+. (b) The composition [0+ x 01] v-constructs the successor of any number x. (c) The closure x [0+ x 01] constructs the successor function. (d) The composition of this closure with 05, i.e., [ x [0+ x 01] 05], constructs the number 6. (e) The composition [0: x 00] does not v-construct anything for any valuation of x;it is improper. (f) The closure x [0: x 00] is not improper, as it constructs something, even though it is only a degenerate function, viz. one undefined at all its arguments.
The constructions 0+, [0+ x 01], x [0+ x 01], [ x [0+ x 01] 05], [0: x 00], x [0: x 00], all mentioned above, are members of *1. When IMPROPER is a set of v-improper constructions of order 1, i.e., when IMPROPER is an object of type ( *1), the composition [0IMPROPER 0[0: x 00]] is a member of type *2, and itconstructs the truth-value True. The constituent 0[0: x 00] of this composition (a member of type *2) is an atomic proper construction that constructs [0: x 00], a member of *1. It is atomic, because the construction [0: x 00] is not used here as a constituent but only mentioned as an input object. For further details, see [6, 26].
If ARITHMETIC is a set of arithmetic functions, then the composition [0ARITHMETIC 2 c] v-constructs True if c v–constructs[ x [0+ x 01]]. The double execution 2 cv-constructs what is v-constructed by [ x [0+ x 01]], i.e., the arithmetic successor function.
Definition 3 (( -)intension,( -)extension)
( -)intensions are members of a type ( ), i.e., functions from possible worlds to the arbitrary type . ( -)extensions are members of the type , where is not equal to ( ) for any , i.e., extensions are not functions from possible worlds.
Remark Intensions are frequently functions of the type (( ) ), i.e., functions from possible worlds to chronologies of the type (in symbols: ), where a chronology is a function of type ( ).
Examples of types
being happy is a property of individuals / ( ) .
The president of the Czech Republic is an individual office (‘individual concept’)/ . That Charles is happy is a proposition / .
Knowing is an attitude of an individual to a construction, i.e., a relation that is a higherorder intension / ( n)
3.4 Semantic Analysis
We adhere to the constraint on natural-language analysis dictated by the principle of subject matter: an admissible analysis of an expression E is a construction C such that C uses, as its constituents, constructions of just those objects that E mentions, i.e., only the objects denoted by sub-expressions of E. Any such analysis is the best analysis of E, relative to a set of atomic constructions (see [9], [22]). The principle is central to our general three-step method of logical analysis of language:
(i) Type-theoretical analysis Assign types to the objects mentioned, i.e., only those that are denoted by sub-expressions of E, and do not omit any semantically self-contained subexpression of E, i.e., use all of them.
(ii) Synthesis Compose constructions of these objects so as to construct the object D denoted by E.
(iii) Type checking Use the assigned types for control so as to check whether the various types are compatible and, furthermore, produce the right type of object in the manner prescribed by the analysis.
A construction of an intension is of the form w t X, w , t . If C is a construction of an intension Int, the composition [[C w] t] the intensional descent of Int to its extension (if any) at w,t will be abbreviated Cwt
Example of analysis We are going to analyse the sentence, “The President of USA is G.W.Bush”.
(i’) President-of / ( ) (an empirical function that dependently on the states of affairs assigns an individual to an individual), USA / (for the sake of simplicity), the The President of USA / — an individual office, G.W.Bush / — (for the sake of simplicity), = / ( ) the identity of individuals. The whole sentence denotes a proposition /
(ii’) w t [0President-ofwt 0USA] (the individual office – role PUSA)
[ w t [0President-ofwt 0USA]]wt (the occupant of the office PUSA)
[0= [ w t [0President-ofwt 0USA]]wt 0G.W.Bush]
w t [0= [ w t [0President-ofwt 0USA]]wt 0G.W.Bush] .
(iii’) w t [0= [ w t [0President-ofwt 0USA]]wt 0G.W.Bush] ( ) ( )
Abstracting over t: ( )
Abstracting over w: (( ) ), i.e., .
When being the President of USA, G.W. Bush is identical with the individual that holds the office PUSA. If, however, John Kerry wanted to become the President of USA, he certainly did not want to become G.W. Bush. He simply wanted to hold the office PUSA, i.e., he is related not to the individual, but to the individual office. Now the paradoxical argument is easily solved away:
“John Kerry wanted to become the President of USA”
w t [0Wantwt 0J.Kerry [ w t [0Becomewt 0J.Kerry w t [0President-ofwt 0USA]]]], where Want / ( ) , Become / ( ) .
The construction w t [0President-ofwt 0USA], i.e., a concept of the president of USA, is in the de dicto supposition [6], the undesirable substitution is blocked. Knowing is a relation-in-intension of an agent a to the meaning of the embedded clause, i.e., to the construction of the respective proposition [8]. Thus when the President of USA knows that John Kerry wanted to become the President of USA, he is related to the construction of the proposition, and the former concept of the president of USA is used de re, the latter de dicto.
The whole argument is analysed as follows:
w t [0= [ w t [0President-ofwt 0USA]]wt 0G.W.Bush]
w t [0Knowwt [ w t [0President-ofwt 0USA]]wt 0[ w t [0Wantwt 0J.Kerry w t [0Becomewt 0J.Kerry w t [0President-ofwt 0USA]]]]]
