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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 261 (19 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...
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 185 (12 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 Terminological Knowledge Representation System with Complete Inference Algorithms
 In Proceedings of the First International Workshop on Processing Declarative Knowledge
, 1991
"... The knowledge representation system klone rst appeared in 1977. Since then many systems based on the idea of klone have been built. The formal modeltheoretic semantics which has been introduced for klone languages [BL84] provides means for investigating soundness and completeness of inference al ..."
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Cited by 95 (18 self)
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The knowledge representation system klone rst appeared in 1977. Since then many systems based on the idea of klone have been built. The formal modeltheoretic semantics which has been introduced for klone languages [BL84] provides means for investigating soundness and completeness of inference algorithms. It turned out that almost all implemented klone systems such as back, kltwo, loom, nikl, sbone use sound but incomplete algorithms.
Reasoning in Description Logics
, 1996
"... ion/Subsumption, has been broadly exploited in actual systems (see Kindermann 1990, Quantz and Kindermann 1990, Nebel 1990a). The Abstraction/Subsumption idea is applicable to a number of languages. However, there are cases where, in order to check whether \Sigma j= D(a), it is necessary to conside ..."
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Cited by 59 (0 self)
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ion/Subsumption, has been broadly exploited in actual systems (see Kindermann 1990, Quantz and Kindermann 1990, Nebel 1990a). The Abstraction/Subsumption idea is applicable to a number of languages. However, there are cases where, in order to check whether \Sigma j= D(a), it is necessary to consider assertions about other objects in the knowledge base different from a, and the above method is no longer applicable. We discuss these cases in Sections 4.2 and 4.3. Subsequently, we show in Section 4.4 how to enrich concept languages with an epistemic operator, so as to distinguish the knowledge about the world and knowledge about the state of the knowledge base. In particular, we demonstrate that the epistemic operator introduces a sophisticated query mechanism that can be used to decrease the complexity of Instance Checking. 4.1 Complexity Measures The complexity of a problem is generally measured with respect to the size of its whole input. For instance, in Section 3 the complexity of...
An Empirical Analysis of Terminological Representation Systems
 Artificial Intelligence
, 1994
"... The family of terminological representation systems has its roots in the representation system klone. Since the development of klone more than a dozen similar representation systems have been developed by various research groups. These systems vary along a number of dimensions. In this paper, we p ..."
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Cited by 44 (2 self)
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The family of terminological representation systems has its roots in the representation system klone. Since the development of klone more than a dozen similar representation systems have been developed by various research groups. These systems vary along a number of dimensions. In this paper, we present the results of an empirical analysis of six such systems. Surprisingly, the systems turned out to be quite diverse, leading to problems when transporting knowledge bases from one system to another. Additionally, the runtime performance between different systems and knowledge bases varied more than we expected. Finally, our empirical runtime performance results give an idea of what runtime performance to expect from such representation systems. These findings complement previously reported analytical results about the computational complexity of reasoning in such systems.
Reasoning with inclusion axioms in description logics: Algorithms and complexity
 In Wahlster, W. (Ed.), Proc. of the 12th European Conf. on Artificial Intelligence (ECAI96
, 1996
"... Abstract. The computational complexity of reasoning on pure concept expressions has been characterized completely for all relevant description logics. On the contrary, reasoning in the presence of schema axioms is not so well understood and far from being settled completely. An important class of sc ..."
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Cited by 36 (10 self)
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Abstract. The computational complexity of reasoning on pure concept expressions has been characterized completely for all relevant description logics. On the contrary, reasoning in the presence of schema axioms is not so well understood and far from being settled completely. An important class of schemata is that of primitive schemata (in which the schema axioms express only necessary conditions) possibly containing cycles. In this paper we provide, for a relevant class of description logics, a complete characterization of computational complexity of reasoning in these types of schemata, both in the presence and in the absence of cycles. The results are obtained by devising reasoning procedures, establishing direct reductions to show lower bounds, and introducing a general technique by which the constructor for existential quantification can be removed without influencing the result of reasoning. 1
Finite model reasoning in description logics
 In Proc. of the 5th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR96
, 1996
"... For the basic Description Logics reasoning with respect to finite models amounts to reasoning with respect to arbitrary ones, but finiteness of the domain needs to be considered if expressivity is increased and the finite model property fails. Procedures for reasoning with respect to arbitrary model ..."
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Cited by 36 (16 self)
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For the basic Description Logics reasoning with respect to finite models amounts to reasoning with respect to arbitrary ones, but finiteness of the domain needs to be considered if expressivity is increased and the finite model property fails. Procedures for reasoning with respect to arbitrary models in very expressive Description Logics have been developed, but these are not directly applicable in the finite case. We first show that we can nevertheless capture a restricted form of finiteness and represent finite modeling structures such as lists and trees, while still reasoning with respect to arbitrary models. The main result of this paper is a procedure to reason with respect to finite models in an expressive Description Logic equipped with inverse roles, cardinality constraints, and in which arbitrary inclusions between concepts can be specified without any restriction. This provides the necessary expressivity to go beyond most semantic and objectoriented Database models, and capture several useful extensions. 1
Artificial Intelligence: A Computational Perspective
 Essentials in Knowledge Representation
, 1994
"... Although the computational perspective on cognitive tasks has always played a major role in Artificial Intelligence, the interest in the precise determination of the computational costs that are required for solving typical AI problems has grown only recently. In this paper, we will describe what in ..."
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Cited by 31 (1 self)
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Although the computational perspective on cognitive tasks has always played a major role in Artificial Intelligence, the interest in the precise determination of the computational costs that are required for solving typical AI problems has grown only recently. In this paper, we will describe what insights a computational complexity analysis can provide and what methods are available to deal with the complexity problem. This work was partially supported by the European Commission as part of DRUMSII, the ESPRIT Basic Research Project P6156. 1 Introduction It is wellknown that typical AI problems, such as natural language understanding, scene interpretation, planning, configuration, or diagnosis are computationally difficult. Hence, it seems to be worthless to analyze the computational complexity of these problems. In fact, some people believe that all AI problems are NPhard or even undecidable. Conceiving AI as a scientific field that has as its goal the analysis and synthesis of...