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96
Query Answering for OWLDL with Rules
 Journal of Web Semantics
, 2004
"... Both OWLDL and functionfree Horn rules are decidable fragments of firstorder logic with interesting, yet orthogonal expressive power. A combination of OWLDL and rules is desirable for the Semantic Web; however, it might easily lead to the undecidability of interesting reasoning problems. Here, w ..."
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Cited by 260 (29 self)
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Both OWLDL and functionfree Horn rules are decidable fragments of firstorder logic with interesting, yet orthogonal expressive power. A combination of OWLDL and rules is desirable for the Semantic Web; however, it might easily lead to the undecidability of interesting reasoning problems. Here, we present a decidable such combination where rules are required to be DLsafe: each variable in the rule is required to occur in a nonDLatom in the rule body. We discuss the expressive power of such a combination and present an algorithm for query answering in the related logic SHIQ extended with DLsafe rules, based on a reduction to disjunctive programs.
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 131 (19 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 resolutionbased 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 joinorder optimizations or magic sets. Equally important, the resolutionbased decision procedure we present is for unary coding of numbers worstcase optimal, i.e. it runs in EXPTIME.
Data Complexity of Reasoning in Very Expressive Description Logics
 IN PROC. IJCAI 2005
, 2005
"... Data complexity of reasoning in description logics (DLs) estimates the performance of reasoning algorithms measured in the size of the ABox only. We show that, even for the very expressive DL SHIQ, satisfiability checking is data complete for NP. For applications with large ABoxes, this can be a mor ..."
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Cited by 103 (22 self)
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Data complexity of reasoning in description logics (DLs) estimates the performance of reasoning algorithms measured in the size of the ABox only. We show that, even for the very expressive DL SHIQ, satisfiability checking is data complete for NP. For applications with large ABoxes, this can be a more accurate estimate than the usually considered combined complexity, which is EXPTIMEcomplete. Furthermore, we identify an expressive fragment, HornSHIQ, which is data complete for P, thus being very appealing for practical usage.
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 71 (22 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.
LightWeight Theorem Proving for Debugging and Verifying Units of Code
, 2003
"... Software bugs are very difficult to detect even in small units of code. Several techniques to debug or prove correct such units are based on the generation of a set of formulae whose unsatisfiability reveals the presence of an error. These techniques assume the availability of a theorem prover capab ..."
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Cited by 49 (27 self)
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Software bugs are very difficult to detect even in small units of code. Several techniques to debug or prove correct such units are based on the generation of a set of formulae whose unsatisfiability reveals the presence of an error. These techniques assume the availability of a theorem prover capable of automatically discharging the resulting proof obligations. Building such a tool is a difficult, long, and errorprone activity. In this paper, we describe techniques to build provers which are highly automatic and flexible by combining stateoftheart superposition theorem provers and BDDs. We report experimental results on formulae extracted from the debugging of C functions manipulating pointers showing that an implementation of our techniques can discharge proof obligations which cannot be handled by Simplify (the theorem prover used in the ESC/Java tool) and performs much better on others. 1.
On the Properties of Metamodeling in OWL
 In 4th Int. Semantic Web Conf. (ISWC 2005
, 2005
"... Abstract. A common practice in conceptual modeling is to separate the intensional from the extensional model. Although very intuitive, this approach is inadequate for many complex domains, where the borderline between the two models is not clearcut. Therefore, OWLFull, the most expressive of the S ..."
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Cited by 45 (0 self)
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Abstract. A common practice in conceptual modeling is to separate the intensional from the extensional model. Although very intuitive, this approach is inadequate for many complex domains, where the borderline between the two models is not clearcut. Therefore, OWLFull, the most expressive of the Semantic Web ontology languages, allows combining the intensional and the extensional model by a feature we refer to as metamodeling. In this paper, we show that the semantics of metamodeling adopted in OWLFull leads to undecidability of basic inference problems, due to free mixing of logical and metalogical symbols. Based on this result, we propose two alternative semantics for metamodeling: the contextual and the HiLog semantics. We show that SHOIQ — a description logic underlying OWLDL — extended with metamodeling under either semantics is decidable. Finally, we show how the latter semantics can be used in practice to axiomatize the logical interaction between concepts and metaconcepts. 1