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Bayesian Description Logics. In:
 Proc. of DL’14. CEUR Workshop Proceedings,
, 2014
"... Abstract This chapter considers, on the one hand, extensions of Description Logics by features not available in the basic framework, but considered important for using Description Logics as a modeling language. In particular, it addresses the extensions concerning: concrete domain constraints; moda ..."
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Cited by 394 (49 self)
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Abstract This chapter considers, on the one hand, extensions of Description Logics by features not available in the basic framework, but considered important for using Description Logics as a modeling language. In particular, it addresses the extensions concerning: concrete domain constraints; modal, epistemic, and temporal operators; probabilities and fuzzy logic; and defaults. On the other hand, it considers nonstandard inference problems for Description Logics, i.e., inference problems thatunlike subsumption or instance checkingare not available in all systems, but have turned out to be useful in applications. In particular, it addresses the nonstandard inference problems: least common subsumer and most specific concept; unification and matching of concepts; and rewriting.
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 260 (26 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.
Hypertableau Reasoning for Description Logics
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2007
"... We present a novel reasoning calculus for the description logic SHOIQ + —a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableaubased reasoning ca ..."
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Cited by 132 (26 self)
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We present a novel reasoning calculus for the description logic SHOIQ + —a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableaubased reasoning calculi used in stateoftheart reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions—a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over stateoftheart reasoners on several wellknown ontologies.
Optimized Reasoning in Description Logics using hypertableaux
"... We present a novel reasoning calculus for Description Logics (DLs)—knowledge representation formalisms with applications in areas such as the Semantic Web. In order to reduce the nondeterminism due to general inclusion axioms, we base our calculus on hypertableau and hyperresolution calculi, which ..."
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Cited by 67 (12 self)
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We present a novel reasoning calculus for Description Logics (DLs)—knowledge representation formalisms with applications in areas such as the Semantic Web. In order to reduce the nondeterminism due to general inclusion axioms, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. To prevent the calculus from generating large models, we introduce “anywhere” pairwise blocking. Our preliminary implementation shows significant performance improvements on several wellknown ontologies. To the best of our knowledge, our reasoner is currently the only one that can classify the original version of the GALEN terminology.
Reasoning with Axioms: Theory and Practice
 IN PROC. OF THE 7TH INT. CONF. ON PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING (KR 2000
, 2000
"... When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively inexpressive logics, and it is essential to deal with such a ..."
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Cited by 47 (17 self)
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When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively inexpressive logics, and it is essential to deal with such axioms in an ecient manner if implemented systems are to be effective in real applications. This is particularly relevant to Description Logics, where subsumption reasoning with respect to a terminology is a fundamental problem. Two optimisation techniques that have proved to be particularly eective in dealing with terminologies are lazy unfolding and absorption. In this paper we seek to improve our theoretical understanding of these important techniques. We define a formal framework that allows the techniques to be precisely described, establish conditions under which they can be safely applied, and prove that, provided these conditions are respected, subsumption testing algo...
Deciding regular grammar logics with converse through firstorder logic
 JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
, 2005
"... ..."
EXPTime tableaux with global caching for description logics with transitive roles, inverse roles and role hierarchies
 IN PROC. TABLEAUX 2007, AIX EN PROVENCE
, 2007
"... The description logic SHI extends the basic description logic ALC with transitive roles, role hierarchies and inverse roles. The known tableaubased decision procedure [9] for SHI exhibit (at least) NEXPTIME behaviour even though SHI is known to be EXPTIMEcomplete. The automatabased algorithms fo ..."
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Cited by 28 (13 self)
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The description logic SHI extends the basic description logic ALC with transitive roles, role hierarchies and inverse roles. The known tableaubased decision procedure [9] for SHI exhibit (at least) NEXPTIME behaviour even though SHI is known to be EXPTIMEcomplete. The automatabased algorithms for SHI often yield optimal worstcase complexity results, but do not behave well in practice since good optimisations for them have yet to be found. We extend our method for global caching in ALC to SHI by adding analytic cut rules, thereby giving the first EXPTIME tableaubased decision procedure for SHI, and showing one way to incorporate global caching and inverse roles.
Rational closure for defeasible description logics.
 Logics in Artificial Intelligence  Proceedings of the12th European Conference (JELIA 2010). Volume 6341 of Lecture Notes in Computer Science (LNCS).,
, 2010
"... Abstract. In the field of nonmonotonic logics, the notion of rational closure is acknowledged as a landmark, and we are going to see that such a construction can be characterised by means of a simple method in the context of propositional logic. We then propose an application of our approach to ra ..."
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Cited by 26 (4 self)
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Abstract. In the field of nonmonotonic logics, the notion of rational closure is acknowledged as a landmark, and we are going to see that such a construction can be characterised by means of a simple method in the context of propositional logic. We then propose an application of our approach to rational closure in the field of Description Logics, an important knowledge representation formalism, and provide a simple decision procedure for this case.
Implementation and Optimisation Techniques
, 2003
"... This chapter will discuss the implementation of the reasoning services which form the core of Description Logic 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 ..."
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Cited by 25 (5 self)
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This chapter will discuss the implementation of the reasoning services which form the core of Description Logic 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 worstcase complexities, this can only be achieved by employing highly optimised 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 unoptimised reasoning is hopelessly intractable.
On the relation of resolution and tableaux proof systems for description logics
 In Proc. IJCAI'99
, 1999
"... This paper investigates the relationship between resolution and tableaux proof system for the satisfiability of general knowledge bases in the description logic We show that resolution proof systems can polynornially simulate their tableaux counterpart. Our resolution proof system is based on a sele ..."
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Cited by 23 (10 self)
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This paper investigates the relationship between resolution and tableaux proof system for the satisfiability of general knowledge bases in the description logic We show that resolution proof systems can polynornially simulate their tableaux counterpart. Our resolution proof system is based on a selection refinement and utilises standard redundancy elimination criteria to ensure termination. 1