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A Scheme for Integrating Concrete Domains into Concept Languages
, 1991
"... A drawback which concept languages based on klone have is that all the terminological knowledge has to be defined on an abstract logical level. In many applications, one would like to be able to refer to concrete domains and predicates on these domains when defining concepts. Examples for such conc ..."
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Cited by 284 (22 self)
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A drawback which concept languages based on klone have is that all the terminological knowledge has to be defined on an abstract logical level. In many applications, one would like to be able to refer to concrete domains and predicates on these domains when defining concepts. Examples for such concrete domains are the integers, the real numbers, or also nonarithmetic domains, and predicates could be equality, inequality, or more complex predicates. In the present paper we shall propose a scheme for integrating such concrete domains into concept languages rather than describing a particular extension by some specific concrete domain. We shall define a terminological and an assertional language, and consider the important inference problems such as subsumption, instantiation, and consistency. The formal semantics as well as the reasoning algorithms are given on the scheme level. In contrast to existing klone based systems, these algorithms will be not only sound but also complete. The...
Using an Expressive Description Logic: FaCT or Fiction?
 In Proc. of KR98
, 1998
"... Description Logics form a family of formalisms closely related to semantic networks but with the distinguishing characteristic that the semantics of the concept description language is formally defined, so that the subsumption relationship between two concept descriptions can be computed by a suitab ..."
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Cited by 274 (53 self)
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Description Logics form a family of formalisms closely related to semantic networks but with the distinguishing characteristic that the semantics of the concept description language is formally defined, so that the subsumption relationship between two concept descriptions can be computed by a suitable algorithm. Description Logics have proved useful in a range of applications but their wider acceptance has been hindered by their limited expressiveness and the intractability of their subsumption algorithms. This paper addresses both these issues by describing a sound and complete tableaux subsumption testing algorithm for a relatively expressive Description Logic which, in spite of the logic's worst case complexity, has been shown to perform well in realistic applications. 1 INTRODUCTION Description Logics (DLs) form a family of formalisms which have grown out of knowledge representation techniques using frames and semantic networks
Tableau Algorithms for Description Logics
 STUDIA LOGICA
, 2000
"... Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Klone. During the last decade, it has been shown that the important reasoning problems (like subsumption and satisfiability) in a great variety of descriptio ..."
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Cited by 265 (27 self)
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Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Klone. During the last decade, it has been shown that the important reasoning problems (like subsumption and satisfiability) in a great variety of description logics can be decided using tableaulike algorithms. This is not very surprising since description logics have turned out to be closely related to propositional modal logics and logics of programs (such as propositional dynamic logic), for which tableau procedures have been quite successful. Nevertheless, due to different underlying intuitions and applications, most description logics differ significantly from runofthemill modal and program logics. Consequently, the research on tableau algorithms in description logics led to new techniques and results, which are, however, also of interest for modal logicians. In this article, we will focus on three features that play an important role in description logics (number restrictions, terminological axioms, and role constructors), and show how they can be taken into account by tableau algorithms.
The Complexity of Concept Languages
, 1995
"... The basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies, and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called concept ..."
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Cited by 248 (36 self)
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The basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies, and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called concept language (or description logic), which is given welldefined settheoretic semantics. The efficiency of reasoning has often been advocated as a primary motivation for the use of such systems. Deduction methods and computational properties of reasoning problems in concept languages are the subject of this paper. The main contributions of the paper are: (1) a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages; (2) the algorithms for these inferences that comply with the worstcase complexity of the reasoning task they perform.
Decidable reasoning in terminological knowledge representation systems
 Journal of Artificial Intelligence Research
, 1993
"... Terminological Knowledge Representation Systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). The TKRS we consider in this paper is of practical interest since it goes beyond the capabilities of presently available TKRSs. ..."
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Cited by 204 (13 self)
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Terminological Knowledge Representation Systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). The TKRS we consider in this paper is of practical interest since it goes beyond the capabilities of presently available TKRSs. First, our TKRS is equipped with a highly expressive concept, language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, it allows one to express inclusion statements between general concepts, in particular to express terminological cycles. We provide a sound, complete and terminating calculus for reasoning in ALCNRknowledge bases based on the general technique of constraint systems.
A Semantics and Complete Algorithm for Subsumption in the CLASSIC Description Logic
 Journal of Artificial Intelligence Research
, 1994
"... This paper analyzes the correctness of the subsumption algorithm used in classic, a description logicbased knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in classic descriptions, the developers have had to use an algori ..."
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Cited by 174 (14 self)
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This paper analyzes the correctness of the subsumption algorithm used in classic, a description logicbased knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in classic descriptions, the developers have had to use an algorithm that is incomplete with respect to the standard, modeltheoretic semantics for description logics. We provide a variant semantics for descriptions with respect to which the current implementation is complete, and which can be independently motivated. The soundness and completeness of the polynomialtime subsumption algorithm is established using description graphs, which are an abstracted version of the implementation structures used in classic, and are of independent interest. 1. Introduction to Description Logics Data and knowledge bases are models of some part of the natural world. Such models are often built from individual objects that are interrelated by relationships and g...
Embedding Defaults into Terminological Knowledge Representation Formalisms
 Journal of Automated Reasoning
, 1995
"... We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of firstorder logic. Semant ..."
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Cited by 156 (8 self)
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We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of firstorder logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter's semantics. On the algorithmic side, we show that this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are only applied to individuals that are explicitly presen...
Econnections of abstract description systems
"... Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because nontrivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is chal ..."
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Cited by 126 (34 self)
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Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because nontrivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is challenging because the computational behavior of the resulting hybrids is often much worse than the behavior of their components. In this paper, we propose a new combination method which is computationally robust in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows nontrivial interactions between the combined components. The new method, called Econnection, is defined in terms of abstract description systems (ADSs), a common generalization of description logics, many logics of time and space, as well as modal and epistemic logics. The basic idea of Econnections is that the interpretation domains of n combined systems are disjoint, and that these domains are connected by means of nary ‘link relations. ’ We define several natural variants of Econnections and study indepth the transfer of decidability from the component systems to their Econnections. Key words: description logics, temporal logics, spatial logics, combining logics, decidability.