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Reducing SHIQ − Description Logic to Disjunctive Datalog Programs
, 2004
"... As applications of description logics proliferate, efficient reasoning with large ABoxes (sets of individuals with descriptions) becomes ever more important. Motivated by the prospects of reusing optimization techniques from deductive databases, in this paper, we present a novel approach to checking ..."
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Cited by 143 (20 self)
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As applications of description logics proliferate, efficient reasoning with large ABoxes (sets of individuals with descriptions) becomes ever more important. Motivated by the prospects of reusing optimization techniques from deductive databases, in this paper, we present a novel approach to checking consistency of ABoxes, instance checking and query answering, w.r.t. ontologies formulated using a slight restriction of the description logic SHIQ. Our approach proceeds in three steps: (i) the ontology is translated into firstorder clauses, (ii) TBox and RBox clauses are saturated using a resolution-based decision procedure, and (iii) the saturated set of clauses is translated into a disjunctive datalog program. Thus, query answering can be performed using the resulting program, while applying all existing optimization techniques, such as join-order optimizations or magic sets. Equally important, the resolution-based decision procedure we present is for unary coding of numbers worst-case optimal, i.e. it runs in EXPTIME.
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 tableau-based 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 tableau-based reasoning calculi used in state-of-the-art 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 state-of-the-art reasoners on several well-known 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 well-known ontologies. To the best of our knowledge, our reasoner is currently the only one that can classify the original version of the GALEN terminology.
Deciding regular grammar logics with converse through first-order logic
- JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
, 2005
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A resolution-based decision procedure for SHOIQ
- Proc. of the 3rd Int. Joint Conf. on Automated Reasoning (IJCAR 2006), volume 4130 of LNAI
, 2006
"... Abstract. We present a resolution-based decision procedure for the description logic SHOIQ—the logic underlying the Semantic Web ontology language OWL-DL. Our procedure is goal-oriented, and it naturally extends a similar procedure for SHIQ, which has proven itself in practice. Applying existing tec ..."
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Cited by 30 (6 self)
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Abstract. We present a resolution-based decision procedure for the description logic SHOIQ—the logic underlying the Semantic Web ontology language OWL-DL. Our procedure is goal-oriented, and it naturally extends a similar procedure for SHIQ, which has proven itself in practice. Applying existing techniques for deriving saturation-based decision procedures to SHOIQ is not straightforward due to nominals, number restrictions, and inverse roles—a combination known to cause termination problems. We overcome this difficulty by using the basic superposition calculus, extended with custom simplification rules. 1
Representing Ontologies Using Description Logics, Description Graphs, and Rules
- Artificial Intelligence
"... Description logics (DLs) are a family of state-of-the-art knowledge representation languages, and their expressive power has been carefully crafted to provide useful knowledge modeling primitives while allowing for practically effective decision procedures for the basic reasoning problems. Recent ex ..."
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Cited by 28 (6 self)
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Description logics (DLs) are a family of state-of-the-art knowledge representation languages, and their expressive power has been carefully crafted to provide useful knowledge modeling primitives while allowing for practically effective decision procedures for the basic reasoning problems. Recent experience with DLs, however, has shown that their expressivity is often insufficient to accurately describe structured objects—objects whose parts are interconnected in arbitrary, rather than tree-like ways. DL knowledge bases describing structured objects are therefore usually underconstrained, which precludes the entailment of certain consequences and causes performance problems during reasoning. To address this problem, we propose an extension of DL languages with description graphs—a knowledge modeling construct that can accurately describe objects with parts connected in arbitrary ways. Furthermore, to enable modeling the conditional aspects of structured objects, we also extend DLs with rules. We present an in-depth study of the computational properties of such a formalism. In particular, we first identify the sources of undecidability of the general, unrestricted formalism. Based on that analysis, we then investigate several restrictions of the general formalism that make reasoning decidable. We present practical evidence that such a logic can be used to model nontrivial structured objects. Finally, we present a practical decision procedure for our formalism, as well as tight complexity bounds. Key words: knowledge representation, description logics, structured objects, ontologies ⋆ This is an extended version of two papers published at WWW 2008 [29] and KR 2008 [28], respectively. ∗ Corresponding author.
Structured Objects in OWL: Representation and Reasoning
, 2008
"... Applications of semantic technologies often require the representation of and reasoning with structured objects—that is, objects composed of parts connected in complex ways. Although OWL is a general and powerful language, its class descriptions and axioms cannot be used to describe arbitrarily conn ..."
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Cited by 20 (5 self)
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Applications of semantic technologies often require the representation of and reasoning with structured objects—that is, objects composed of parts connected in complex ways. Although OWL is a general and powerful language, its class descriptions and axioms cannot be used to describe arbitrarily connected structures. OWL representation of structured objects can thus be underconstrained, which reduces the inferences that can be drawn and causes performance problems in reasoning. To address these problems, we extend OWL with description graphs, which provide for the description of structured objects in a simple and precise way. To represent conditional aspects of the domain, we also allow for SWRL-like rules over description graphs. Based on a novel observation about the nature of structured objects, we ensure decidability of our formalism. We also present a hypertableau-based decision procedure, which we implemented in the HermiT reasoner. To evaluate its performance, we extracted description graphs from the GALEN and FMA ontologies, classified them successfully, and even detected a modeling error in GALEN. 1
Deciding Expressive Description Logics in the Framework of Resolution
"... We present a decision procedure for the description logic SHIQ based on the basic superposition calculus, and show that it runs in exponential time for unary coding of numbers. To derive our algorithm, we extend basic superposition with a decomposition inference rule, which transforms conclusions of ..."
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Cited by 10 (2 self)
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We present a decision procedure for the description logic SHIQ based on the basic superposition calculus, and show that it runs in exponential time for unary coding of numbers. To derive our algorithm, we extend basic superposition with a decomposition inference rule, which transforms conclusions of certain inferences into equivalent, but simpler clauses. This rule can be used for general first-order theorem proving with any resolution-based calculus compatible with the standard notion of redundancy.
Description logics and disjunctive datalog -- the story so far
- PROC. INTERNATIONAL WORKSHOP ON DESCRIPTION LOGICS
, 2005
"... In this paper we present an overview of our recent work on the relationship between description logics and disjunctive datalog. In particular, we reduce satisfiability and instance checking in SHIQ to corresponding problems in disjunctive datalog. This allows us to apply practically successful deduc ..."
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Cited by 7 (0 self)
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In this paper we present an overview of our recent work on the relationship between description logics and disjunctive datalog. In particular, we reduce satisfiability and instance checking in SHIQ to corresponding problems in disjunctive datalog. This allows us to apply practically successful deductive database optimization techniques, such as magic sets. Interestingly, the reduction also allows us to obtain novel theoretical results on description logics. In particular, we show that the data complexity of reasoning in SHIQ is in NP, and we define a fragment called Horn-SHIQ for which the data complexity is in P. Finally, the reduction provides a basis for query answering in an extension of SHIQ with so-called DL-safe rules.
First-order resolution methods for modal logics
- In Volume in Memoriam of Harald Ganzinger, LNCS
, 2006
"... Abstract. In this paper we give an overview of results for modal logic which can be shown using techniques and methods from first-order logic and resolution. Because of the breadth of the area and the many applications we focus on the use of first-order resolution methods for modal logics. In additi ..."
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Cited by 7 (4 self)
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Abstract. In this paper we give an overview of results for modal logic which can be shown using techniques and methods from first-order logic and resolution. Because of the breadth of the area and the many applications we focus on the use of first-order resolution methods for modal logics. In addition to traditional propositional modal logics we consider more expressive PDL-like dynamic modal logics which are closely related to description logics. Without going into too much detail, we survey different ways of translating modal logics into first-order logic, we explore different ways of using first-order resolution theorem provers, and we discuss a variety of results which have been obtained in the setting of first-order resolution. 1
