27 results in The Description Logic Handbook
2 - Basic Description Logics
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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Abstract
This chapter provides an introduction to Description Logics as a formal language for representing knowledge and reasoning about it. It first gives a short overview of the ideas underlying Description Logics. Then it introduces syntax and semantics, covering the basic constructors that are used in systems or have been introduced in the literature, and the way these constructors can be used to build knowledge bases. Finally, it defines the typical inference problems, shows how they are interrelated, and describes different approaches for effectively solving these problems. Some of the topics that are only briefly mentioned in this chapter will be treated in more detail in subsequent chapters.
Introduction
As sketched in the previous chapter, Description Logics is the most recent name for a family of knowledge representation (KR) formalisms that represent the knowledge of an application domain (the “world”) by first defining the relevant concepts of the domain (its terminology), and then using these concepts to specify properties of objects and individuals occurring in the domain (the world description). As the name Description Logics indicates, one of the characteristics of these languages is that, unlike some of their predecessors, they are equipped with a formal, logic-based semantics. Another distinguished feature is the emphasis on reasoning as a central service: reasoning allows one to infer implicitly represented knowledge from the knowledge that is explicitly contained in the knowledge base.
13 - Medical Informatics
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- By A. Rector
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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Description Logics and related formalisms are being applied in at least five applications in medical informatics – terminology, intelligent user interfaces, decision support and semantic indexing, language technology, and systems integration. Important issues include size, complexity, connectivity, and the wide range of granularity required – medical terminologies require on the order of 250,000 concepts, some involving a dozen or more conjuncts with deep nesting; the nature of anatomy and physiology is that everything connects to everything else; and notions to be represented range from psychology to molecular biology. Technical issues for expressivity have focused on problems of part–whole relations and the need to provide “frame-like” functionality – i.e., the ability to determine efficiently what can sensibly be said about any particular concept and means of handling at least limited cases of defaults with exceptions. There are also significant problems with “semantic normalization” and “clinical pragmatics” because understanding medical notions often depends on implicit knowledge and some notions defy easy logical formulation. The two best-known efforts – Open Galen and Snomed-rt – both use idiosyncratic Description Logics with generally limited expressivity but specialized extensions to cope with issues around part–whole and other transitive relations. There is also a conflict between the needs for re-use and the requirement for easy understandability by domain expert authors. OpenGalen has coped with this conflict by introducing a layered architecture with a high level “Intermediate Representation” which insulates authors from the details of the Description Logic, which is treated as an “assembly language” rather than the primary medium for expressing the ontology.
Part II - Implementation
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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9 - Implementation and Optimization Techniques
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- By I. Horrocks
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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This chapter will discuss the implementation of the reasoning services which form the core of DL-based knowledge representation systems. To be useful in realistic applications, such systems need both expressive logics and fast reasoners. As expressive logics inevitably have high worst-case complexities, this can only be achieved by employing highly optimized implementations of suitable reasoning algorithms. Systems based on such implementations have demonstrated that they can perform well with problems that occur in realistic applications, including problems where unoptimized reasoning is hopelessly intractable.
Introduction
The usefulness of Description Logics in applications has been hindered by the basic conflict between expressiveness and tractability. Realistic applications typically require both expressive logics, with inevitably high worst-case complexities for their decision procedures, and acceptable performance from the reasoning services. Although the definition of acceptable may vary widely from application to application, early experiments with Description Logics indicated that, in practice, performance was a serious problem, even for logics with relatively limited expressive powers [Heinsohn et al., 1992].
On the other hand, theoretical work has continued to extend our understanding of the boundaries of decidability in Description Logics, and has led to the development of sound and complete reasoning algorithms for much more expressive logics. The expressive power of these logics goes a long way towards addressing the criticisms leveled at Description Logics in traditional applications such as ontological engineering [Doyle and Patil, 1991] and is sufficient to suggest that they could be useful in several exciting new application domains, for example reasoning about database schemas and queries [Calvanese et al., 1998f; 1998a] and providing reasoning support for the so-called Semantic Web [Decker et al., 2000; Bechhofer et al., 2001b].
14 - OWL: a Description-Logic-Based Ontology Language for the Semantic Web
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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It has long been realized that the web could benefit from having its content understandable and available in a machine processable form. The Semantic Web aims to achieve this via annotations that use terms defined in ontologies to give well defined meaning to web accessible information and services. OWL, the ontology language recommended by the W3C for this purpose, was heavily influenced by Description Logic research. In this chapter we review briefly some early efforts that combine Description Logics and the web, including predecessors of OWL such as OIL and DAML+OIL. We then go on to describe OWL in some detail, including the various influences on its design, its relationship with RDFS, its syntax and semantics, and a range of tools and applications.
Background and history
The World Wide Web, while wildly successful in growth, may be viewed as being limited by its reliance on languages such as HTML that are focused on presentation (i.e., text formatting) rather than content. Languages such as XML do add some support for capturing the meaning of web content (instead of simply how to render it in a browser), but more is needed in order to support intelligent applications that can better exploit the ever increasing range of information and services accessible via the web. Such applications are urgently needed in order to avoid overwhelming users with the sheer volume of information becoming available.
5 - Expressive Description Logics
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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This chapter covers extensions of the basic Description Logics introduced in Chapter 2 by very expressive constructs that require advanced reasoning techniques. In particular, we study reasoning in description logics that include general inclusion axioms, inverse roles, number restrictions, reflexive–transitive closure of roles, fixpoint constructs for recursive definitions, and relations of arbitrary arity. The chapter will also address reasoning w.r.t. knowledge bases including both a TBox and an ABox, and discuss more general ways to treat objects. Since the logics considered in the chapter lack the finite model property, finite model reasoning is of interest and will also be discussed. Finally, we mention several extensions to description logics that lead to undecidability, confirming that the expressive description logics considered in this chapter are close to the boundary between decidability and undecidability.
Introduction
Description Logics have been introduced with the goal of providing a formal reconstruction of frame systems and semantic networks. Initially, the research has concentrated on subsumption of concept expressions. However, for certain applications, it turns out that it is necessary to represent knowledge by means of inclusion axioms without limitation on cycles in the TBox. Therefore, recently there has been a strong interest in the problem of reasoning over knowledge bases of a general form. See Chapters 2, 3, and 4 for more details.
When reasoning over general knowledge bases, it is not possible to gain tractability by limiting the expressive power of the description logic, because the power of arbitrary inclusion axioms in the TBox alone leads to high complexity in the inference mechanisms.
10 - Conceptual Modeling with Description Logics
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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The purpose of the chapter is to help someone familiar with DLs to understand the issues involved in developing an ontology for some universe of discourse, which is to become a conceptual model or knowledge base represented and reasoned about using Description Logics.
We briefly review the purposes and history of conceptual modeling, and then use the domain of a university library to illustrate an approach to conceptual modeling that combines general ideas of object-centered modeling with a look at special modeling/ontological problems, and DL-specific solutions to them.
Among the ontological issues considered are the nature of individuals, concept specialization, non-binary relationships, materialization, aspects of part–whole relationships, and epistemic aspects of individual knowledge.
Background
Information modeling is concerned with the construction of computer-based symbol structures that model some part of the real world. We refer to such symbol structures as information bases, generalizing the term from related terms in Computer Science, such as databases and knowledge bases. Moreover, we shall refer to the part of a real world being modeled by an information base as its universe of discourse (UofD). The information base is checked for consistency, and sometimes queried and updated through special-purpose languages. As with all models, the advantage of information models is that they abstract away irrelevant details, and allow more efficient examination of both the current, as well as past and projected future states of the UofD.
16 - Description Logics for Databases
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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In contrast to the relatively complex information that can be expressed in DL ABoxes (which we might call knowledge or information), databases and other sources such as files, semistructured data, and the World Wide Web provide rather simpler data, which must however be managed effectively. This chapter surveys the major classes of application of Description Logics and their reasoning facilities to the issues of data management, including: (i) expressing the conceptual domain model/ontology of the data source, (ii) integrating multiple data sources, and (iii) expressing and evaluating queries. In each case we utilize the standard properties of Description Logics, such as the ability to express ontologies at a level closer to that of human conceptualization (e.g., representing conceptual schemas), determining consistency of descriptions (e.g., determining if a query or the integration of some schemas is consistent), and automatically classifying descriptions that are definitions (e.g., queries are really definitions, so we can classify them and determine subsumption between them).
Introduction
According to [EIMasri and Navathe, 1994], a database is a coherent collection of related data, which have some “inherent meaning”. Databases are similar to knowledge bases because they are usually used to maintain models of some universe of discourse (UofD). Of course, the purpose of such computer models is to support end-users in finding out things about the world, and therefore it is important to maintain an up-to-date and error-free model.
List of contributors
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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Contents
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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Bibliography
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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4 - Relationships with other Formalisms
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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In this chapter, we are concerned with the relationship between Description Logics and other formalisms, regardless of whether they were designed for knowledge representation issues or not. We concentrate on those representation formalisms that either (1) had or have a strong influence on Description Logics (e.g., modal logics), (2) are closely related to Description Logics for historical reasons (e.g., semantic networks and structured inheritance networks), or (3) have similar expressive power (e.g., semantic data models). There are far more knowledge representation formalisms than those mentioned in this chapter. For example, “verb-centered” graphical formalisms like those introduced by Simmons [1973] are not mentioned since we believe that their relationship with Description Logics is too weak.
AI knowledge representation formalisms
In artificial intelligence (AI), various “non-logical” knowledge representation formalisms were developed, motivated by the belief that classical logic is inadequate for knowledge representation in AI applications. This belief was mainly based upon cognitive experiments carried out with human beings and the wish to have representational formalisms that are close to the representations in human brains. In this section, we discuss some of these formalisms, namely semantic networks, frame systems, and conceptual graphs. The first two formalisms are mainly presented for historical reasons since they can be regarded as ancestors of Description Logics. In contrast, the third formalism can be regarded as a “sibling” of Description Logics since both have similar ancestors and live in the same time.
Appendix: Description Logic Terminology
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- By F. Baader
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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The purpose of this appendix is to introduce (in a compact manner) the syntax and semantics of the most prominent DLs occurring in this handbook. More information and explanations as well as some less familiar Description Logics can be found in the respective chapters. For DL constructors whose semantics cannot be described in a compact manner, we will only introduce the syntax and refer the reader to the respective chapter for the semantics. Following Chapter 2 on basic Description Logics, we will first introduce the basic Description Logic AL, and then describe several of its extensions. Thereby, we will also fix the notation employed in this handbook. Finally, we will comment on the naming schemes for Description Logics that are employed in the literature and in this handbook.
Notational conventions
Before starting with the definitions, let us introduce some notational conventions. The letters A,B will often be used for atomic concepts, and C,D for concept descriptions. For roles, we often use the letters R, S, and for functional roles (features, attributes) the letters f, g. Nonnegative integers (in number restrictions) are often denoted by n,m, and individuals by a, b. In all cases, we may also use subscripts. This convention is followed when defining syntax and semantics and in abstract examples. In concrete examples, the following conventions are used: concept names start with an uppercase letter followed by lowercase letters (e.g., Human, Male), role names (also functional ones) start with a lowercase letter (e.g., hasChild, married To), and individual names are all uppercase (e.g., CHARLES, MARY).
Preface
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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Summary
Knowledge Representation is the field of Artificial Intelligence that focuses on the design of formalisms that are both epistemologically and computationally adequate for expressing knowledge about a particular domain. One of the main lines of investigation has been concerned with the principle that knowledge should be represented by characterizing classes of objects and the relationships between them The organization of the classes used to describe a domain of interest is based on a hierarchical structure, which not only provides an effective and compact representation of information, but also allows the relevant reasoning tasks to be performed in a computationally effective way.
The above principle drove the development of the first frame-based systems and semantic networks in the 1970s. However, these systems were in general not formally defined and the associated reasoning tools were strongly dependent on the implementation strategies. A fundamental step towards a logic-based characterization of required formalisms was accomplished through the work on the Kl-One system, which collected many of the ideas stemming from earlier semantic networks and frame-based systems, and provided a logical basis for interpreting objects, classes (or concepts), and relationships (or links, roles) between them. The first goal of such a logical reconstruction was the precise characterization of the set of constructs used to build class and link expressions. The second goal was to provide reasoning procedures that are sound and complete with respect to the semantics.
11 - Software Engineering
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- By C. A. Welty
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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This chapter reviews the application of Description Logics to software engineering, following a steady evolution of DL-based systems used to support the program understanding process for programmers involved in software maintenance.
Introduction
One of the first large applications of Description Logics was in the area of software engineering. In software, programmers and maintainers of large systems are plagued with information overload. These systems are typically over a million lines of code, some approach fifty million. The size of the workforce dedicated to maintaining these enormous systems is often over a thousand. In addition, turnover is quite high, as is the training investment required to make someone a productive member of the team. This seems, on the surface, to be a problem crying out for a knowledge-based solution, but understanding precisely how Description Logics can play a role requires understanding the basic problems of software engineering “in the large”.
Background
The three principal software maintenance tasks are pro-active (testing), reactive (debugging), and enhancement. Central to effective performance of these tasks is understanding the software. In the 1980s, cognitive studies of programmers involved in program understanding [Soloway et al., 1987] revealed two things:
Programmers typically solve problems by realizing “plans” in their programs. This seems to tie the notion of program understanding to plan recognition [Soloway et al., 1986].
Delocalized plans (plans which are not implemented in localized regions of code) are a serious impediment to plan recognition, for both humans and automated methods [Soloway and Letovsky, 1986].
12 - Configuration
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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Description Logics are used to solve a wide variety of problems, with configuration applications being some of the largest and longest-lived. There is concrete, commercial evidence that shows that DL-based configurators have been successfully fielded for over a decade. Additionally, it appears that configuration applications have a number of characteristics that make them well-suited to DL-based solutions. This chapter will introduce the problem of configuration, describe some requirements of configuration applications that make them candidates for DL-based solutions, show examples of these requirements in a configuration example, and introduce the largest and longest-lived family of DL-based configurators.
Introduction
In order to solve a configuration problem, a configurator (human or machine) must find a set of components that fit together to solve the problem specification. Typically, that means the answer will be a parts list that contains a set of components that work together and that the system comprising the components meets the specification. This task can be relatively simple, such as choosing stereo components in order to create a home stereo system. The problem can also be extremely complex, such as choosing the thousands of components that must work together in order to build complicated telecommunications equipment such as cross-connect devices or switches.
One important factor that makes configuration challenging is that making a choice for one component typically generates constraints on other components as well. For example, a customer who chooses a receiver that only supports up to four speakers may not conveniently support a surround sound system with a subwoofer (since this would require more than four speakers).
8 - Description Logic Systems
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- By R. Möller, V. Haarslev
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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This chapter discusses implemented DL systems that have played or play an important role in the field. It first presents several earlier systems that, although not based on Description Logics, have provided important ideas. These systems include Kl-One, Krypton, Nikl, and Kandor. Then, successor systems are described by classifying them along the characteristics discussed in the previous chapters, addressing the following systems: Classic (“almost” complete, fast); Back, Loom (expressive, incomplete); Kris, Crack (expressive, complete). Finally, a new optimized generation of very expressive but sound and complete DL systems is also introduced. In particular, we focus on the systems Dlp, Fact, and Racer and explain what they can and cannot do.
New light through old windows?
In this chapter a description of the goals behind the development of different DL systems is given from a historical perspective. The description of DL systems allows important insights into the development of the knowledge representation research field as a whole. The design decisions behind the well-known systems which we discuss in this chapter not only reflect the trends in different knowledge representation research areas but also characterize the point of view on knowledge representation that different researchers advocate. The chapter discusses general capabilities of the systems and gives an analysis of the main language features and design decisions behind system architectures. The analysis of current systems in the light of a historical perspective might lead to new ideas for the development of even more powerful DL systems in the future.
7 - From Description Logic Provers to Knowledge Representation Systems
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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A DL-based knowledge representation system is more than an inference engine for a particular Description Logic. A knowledge representation system must provide a number of services to human users, including presentation of the information stored in the system in a manner palatable to users and justification of the inferences performed by the system. If human users cannot understand what the system is doing, then the development of knowledge bases is made much more difficult or even impossible. A knowledge representation system must also provide a number of services to application programs, including access to the basic information stored in the system but also including access to the machinations of the system. If programs cannot easily access and manipulate the information stored in the system, then the development of applications is made much more difficult or even impossible.
Introduction
A DL-based knowledge representation system does not live in a vacuum. It has to be prepared to interact with several sorts of other entities. One class of entities consists of human users who develop knowledge bases using the system. If the system cannot effectively interact with these users then it will be difficult to create knowledge bases in the system, and the system will not be used. Another class of entities consists of programs that use the services of the system to provide information to support applications. If the system cannot effectively interact with these programs then it will be difficult to create applications using the system, and the system will not be used.
Preface to the second edition
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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Summary
Since the publication of the first edition of The Description Logic Handbook in 2003, the interest in Description Logics (DL) has steadily increased. This applies both to the number of active DL researchers working on DL theory and implementations of reasoning services, and to the number of applications based on DL technology. One effect of this growing interest was that the first edition of the Handbook has gone through quite a number of reprints. Another effect is, of course, that in the last three years there have been interesting new developments in the three areas (theory, implementation, and applications) that the Handbook covers. Despite that, we feel that most chapters of the Handbook still provide a good introduction to the field and lay a solid foundation that enables the reader to understand and put into context the research articles describing results since 2003. For this reason, we have decided to leave most of the chapters unchanged.
The principal exception is Chapter 14, which in the first edition was entitled “Digital Libraries and Web-Based Information Systems.” This chapter provided a selected history of the use of Description Logics in web-based information systems, and the developments related to emerging web ontology languages such as OIL and DAML+OIL. Since the writing of this chapter, the new language OWL has been developed and recommended by the World Wide Web consortium as the standard web ontology language for the Semantic Web.
Frontmatter
- Edited by Franz Baader, Technische Universität, Dresden, Diego Calvanese, Freie Universität Bozen, Bolzano, Deborah L. McGuinness, Rensselaer Polytechnic Institute, New York, Daniele Nardi, Università degli Studi di Roma 'La Sapienza', Italy, Peter F. Patel-Schneider , AT&T Bell Laboratories, New Jersey
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