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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 262 (20 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...
Terminological Reasoning is Inherently Intractable
 ARTIFICIAL INTELLIGENCE
, 1990
"... Computational tractability has been a major concern in the area of terminological knowledge representation and reasoning. However, all analyses of the computational complexity of terminological reasoning are based on the hidden assumption that subsumption in terminologies reduces to subsumption of c ..."
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Cited by 147 (11 self)
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Computational tractability has been a major concern in the area of terminological knowledge representation and reasoning. However, all analyses of the computational complexity of terminological reasoning are based on the hidden assumption that subsumption in terminologies reduces to subsumption of concept descriptions without a significant increase in computational complexity. In this paper it will be shown that this assumption, which seems to work in the "normal case," is nevertheless wrong. Subsumption in terminologies turns out to be coNPcomplete for a minimal terminological representation language that is a subset of every useful terminological language.
An Empirical Analysis of Optimization Techniques for Terminological Representation Systems  or: Making KRIS get a move on
, 1992
"... We consider different methods of optimizing the classification process of terminological representation systems, and evaluate their effect on three different types of test data. Though these techniques can probably be found in many existing systems, until now there has been no coherent description o ..."
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Cited by 140 (13 self)
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We consider different methods of optimizing the classification process of terminological representation systems, and evaluate their effect on three different types of test data. Though these techniques can probably be found in many existing systems, until now there has been no coherent description of these techniques and their impact on the performance of a system. One goal of this paper is to make such a description available for future implementors of terminological systems. Building the optimizations that came off best into the kris system greatly enhanced its efficiency.
Computing Least Common Subsumers in Description Logics
 PROCEEDINGS OF THE 10TH NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1992
"... Description logics are a popular formalism for knowledge representation and reasoning. This paper introduces a new operation for description logics: computing the "least common subsumer" of a pair of descriptions. This operation computes the largest set of commonalities between two descriptions. Aft ..."
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Cited by 86 (14 self)
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Description logics are a popular formalism for knowledge representation and reasoning. This paper introduces a new operation for description logics: computing the "least common subsumer" of a pair of descriptions. This operation computes the largest set of commonalities between two descriptions. After arguing for the usefulness of this operation, we analyze it by relating computation of the least common subsumer to the wellunderstood problem of testing subsumption; a close connection is shown in the restricted case of "structural subsumption". We also present a method for computing the least common subsumer of "attribute chain equalities", and analyze the tractability of computing the least common subsumer of a set of descriptionsan important operation in inductive learning.
Computational Complexity of Terminological Reasoning in BACK
 Artificial Intelligence
, 1988
"... Terminological reasoning is a mode of reasoning all hybrid knowledge representation systems based on KLONE rely on. After a short introduction of what terminological reasoning amounts to, it is proven that a complete inference algorithm for the BACK system would be computationally intractable. Inte ..."
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Cited by 61 (11 self)
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Terminological reasoning is a mode of reasoning all hybrid knowledge representation systems based on KLONE rely on. After a short introduction of what terminological reasoning amounts to, it is proven that a complete inference algorithm for the BACK system would be computationally intractable. Interestingly, this result also applies to the KANDOR system, which had been conjectured to realize complete terminological inferences with a tractable algorithm. More generally, together with an earlier paper of Brachman and Levesque it shows that terminological reasoning is intractable for any system using a nontrivial description language. Finally, consequences of this distressing result are briefly discussed. 1 Introduction The BACK system 1 [13] belongs to the class of hybrid knowledge representation systems based on KLONE (cf. the article by Brachman and Schmolze [4]). As in any other system of this family, a framebased description language (henceforth FDL), which can be viewed as a ...
Description Logics are not just for the FlightlessBirds: A New Look at the Utility and Foundations of Description Logics
, 1992
"... This paper presents some of the underlying principles of description logics (also known as terminological logics or klonestyle languages), grounding them in the lattice of terms organized by the socalled "subsumption" relationship. A survey of the increasingly varied uses of description logics, i ..."
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Cited by 17 (3 self)
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This paper presents some of the underlying principles of description logics (also known as terminological logics or klonestyle languages), grounding them in the lattice of terms organized by the socalled "subsumption" relationship. A survey of the increasingly varied uses of description logics, including industrial applications, is presented by considering their role in a number of different operations that one can apply to a knowledge base, including languages for queries, answers, updates, rules, and constraints. Finally, we discuss some of the complexity results related to the logics of descriptions, and survey a spectrum of responses to the many intractability proofs. 1 Introduction A large class of practical computer applications requires managing a symbolic model of an application world, which is updated or queried by users. Database management systems, knowledge representation and reasoning systems, and many objectoriented programming systems, especially ones used for sim...
Hybrid Reasoning in BACK
 Methodologies for Intelligent Systems
, 1988
"... Hybrid knowledge representation formalisms consist of two or more different subformalisms for representing different kinds of knowledge or knowledge in different kinds of representation formats. For a semantically wellfounded hybrid formalism not only a precise semantics for each of the participati ..."
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Cited by 15 (0 self)
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Hybrid knowledge representation formalisms consist of two or more different subformalisms for representing different kinds of knowledge or knowledge in different kinds of representation formats. For a semantically wellfounded hybrid formalism not only a precise semantics for each of the participating subformalisms has to be given but a semantics for the interrelationship between these subformalisms as well. A hybrid representation system therefore has to be implemented as a hybrid reasoning system taken into account these semantic models. The BACK system as an instance of this class of systems will be described with respect to the underlying semantic model and the demands for a reasoning component as one part of the realization of the formalism. The consequences and limits for the implementation of the BACK system are discussed. 1 Introduction Aaron Sloman pointed out very clearly in [22] the need for different knowledge representation formalisms for the adequate representation of a...
Learnability of Description Logics
 IN PROCEEDINGS OF THE FOURTH ANNUAL WORKSHOP ON COMPUTATIONAL LEARNING THEORY
, 1992
"... This paper considers the learnability of subsets of firstorder logic. Prior work has established two boundaries of learnability: Haussler [ 1989 ] has shown that conjunctions in firstorder logic cannot be learned in the Valiant model, even if the form of the conjunction is highly restricted; ..."
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Cited by 9 (5 self)
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This paper considers the learnability of subsets of firstorder logic. Prior work has established two boundaries of learnability: Haussler [ 1989 ] has shown that conjunctions in firstorder logic cannot be learned in the Valiant model, even if the form of the conjunction is highly restricted; on the other hand, Valiant [ 1984 ] has shown that propositional conjunctions are learnable. In this
Issues of Integration and Balancing in Hybrid Knowledge Representation Systems
 Proceedings of the GWAI
, 1987
"... In the last several years the hybrid approach to Knowledge Representation has received much attention, because it was felt that one monolithic knowledge representation formalism cannot meet all representational demands. In this paper we will present one particular hybrid knowledge representation sys ..."
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Cited by 6 (1 self)
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In the last several years the hybrid approach to Knowledge Representation has received much attention, because it was felt that one monolithic knowledge representation formalism cannot meet all representational demands. In this paper we will present one particular hybrid knowledge representation system, BACK, concentrating on matters of how to integrate different subformalisms and their interpretation. In particular, `balancing the expressiveness' of the respective subformalisms and combining the reasoning of the subsystems in a sound way is discussed. This will lead to a new view on the realization inference, first described by Mark, as a process of constraint propagation. 1 Introduction Aaron Sloman pointed out very clearly in [Sloman 85] the need for different knowledge representation formalisms for the adequate representation of a realistic portion of the world. This position contrasting the view that one uniform formalism is sufficient (e.g., [Kowalski 80]) is nowadays widely acc...