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Description Logic Programs: Combining Logic Programs with Description Logic
, 2003
"... We show how to interoperate, semantically and inferentially, between the leading Semantic Web approaches to rules (RuleML Logic Programs) and ontologies (OWL/DAML+OIL Description Logic) via analyzing their expressive intersection. To do so, we define a new intermediate knowledge representation (KR) ..."
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Cited by 397 (41 self)
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We show how to interoperate, semantically and inferentially, between the leading Semantic Web approaches to rules (RuleML Logic Programs) and ontologies (OWL/DAML+OIL Description Logic) via analyzing their expressive intersection. To do so, we define a new intermediate knowledge representation (KR) contained within this intersection: Description Logic Programs (DLP), and the closely related Description Horn Logic (DHL) which is an expressive fragment of firstorder logic (FOL). DLP provides a significant degree of expressiveness, substantially greater than the RDFSchema fragment of Description Logic.
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 224 (28 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.
On the Restraining Power of Guards
 Journal of Symbolic Logic
, 1998
"... Guarded fragments of firstorder logic were recently introduced by Andr'eka, van Benthem and N'emeti; they consist of relational firstorder formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional moda ..."
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Cited by 119 (2 self)
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Guarded fragments of firstorder logic were recently introduced by Andr'eka, van Benthem and N'emeti; they consist of relational firstorder formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful modeltheoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions (on the arity of relation symbols, the quantifier pattern or the number of variables) of almost all other known decidable fragments of firstorder logic. Here, we investigate the computational complexity of these fragments. We prove that the satisfiability problems for the guarded fragment (GF) and the loosely guarded fragment (LGF) of firstorder logic are complete for deterministic double exponential time. For the subfragments that have only a bounded number of variables or only relation symbols of bounded arity, satisfiability is EXPTI...
A tableaux decision procedure for SHOIQ
 In Proc. of the 19th Int. Joint Conf. on Artificial Intelligence (IJCAI
, 2005
"... OWL DL, a new W3C ontology language recommendation, is based on the expressive description logic SHOIN. Although the ontology consistency problem for SHOIN is known to be decidable, up to now there has been no known “practical ” decision procedure, i.e., a goal directed procedure that is likely to p ..."
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Cited by 113 (27 self)
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OWL DL, a new W3C ontology language recommendation, is based on the expressive description logic SHOIN. Although the ontology consistency problem for SHOIN is known to be decidable, up to now there has been no known “practical ” decision procedure, i.e., a goal directed procedure that is likely to perform well with realistic ontology derived problems. We present such a decision procedure (for SHOIQ, a slightly more expressive logic than SHOIN), extending the well known algorithm for SHIQ,
Conjunctive query answering for the description logic SHIQ
, 2007
"... Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, it was an open problem whether conjunctive query answering over DL knowledge bases is decidable if transitive roles are admitted in the q ..."
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Cited by 110 (27 self)
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Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, it was an open problem whether conjunctive query answering over DL knowledge bases is decidable if transitive roles are admitted in the query. In this paper, we consider conjunctive queries over knowledge bases formulated in the popular DL SHIQ and allow transitive roles in both the query and the knowledge base. We show that query answering is decidable and establish the following complexity bounds: regarding combined complexity, we devise a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query. Regarding data complexity, we prove coNPcompleteness. 1
Model Checking Partial State Spaces with 3Valued Temporal Logics (Extended Abstract)
 In Proceedings of the 11th Conference on Computer Aided Verification
, 1999
"... ) Glenn Bruns and Patrice Godefroid Bell Laboratories, Lucent Technologies fgrb,godg@belllabs.com Abstract. We address the problem of relating the result of model checking a partial state space of a system to the properties actually possessed by the system. We represent incomplete state space ..."
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Cited by 96 (7 self)
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) Glenn Bruns and Patrice Godefroid Bell Laboratories, Lucent Technologies fgrb,godg@belllabs.com Abstract. We address the problem of relating the result of model checking a partial state space of a system to the properties actually possessed by the system. We represent incomplete state spaces as partial Kripke structures, and give a 3valued interpretation to modal logic formulas on these structures. The third truth value ? means "unknown whether true or false". We define a preorder on partial Kripke structures that reflects their degree of completeness. We then provide a logical characterization of this preorder. This characterization thus relates properties of less complete structures to properties of more complete structures. We present similar results for labeled transition systems and show a connection to intuitionistic modal logic. We also present a 3valued CTL model checking algorithm, which returns ? only when the partial state space lacks information needed ...
Generalized Model Checking: Reasoning about Partial State Spaces
, 2000
"... We discuss the problem of model checking temporal properties on partial Kripke structures, which were used in [BG99] to represent incomplete state spaces. We first extend the results of [BG99] by showing that the modelchecking problem for any 3valued temporal logic can be reduced to two modelchec ..."
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Cited by 74 (6 self)
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We discuss the problem of model checking temporal properties on partial Kripke structures, which were used in [BG99] to represent incomplete state spaces. We first extend the results of [BG99] by showing that the modelchecking problem for any 3valued temporal logic can be reduced to two modelchecking problems for the corresponding 2valued temporal logic. We then introduce a new semantics for 3valued temporal logics that can give more definite answers than the previous one. With this semantics, the evaluation of a formula OE on a partial Kripke structure M returns the third truth value? (read "unknown") only if there exist Kripke structures M1 and M2 that both complete M and such that M1 satisfies OE while M2 violates OE, hence making the value of OE on M truly unknown. The partial Kripke structure M can thus be viewed as a partial solution to the satisfiability problem which reduces the solution space to complete Kripke structures that are more complete than M wit...
Conditional XPath
 ACM Trans. Database Syst
, 2005
"... Abstract. XPath 1.0 is a variable free language designed to specify paths between nodes in XML documents. Such paths can alternatively be specified in firstorder logic. The logical abstraction of XPath 1.0, usually called Navigational or Core XPath, is not powerful enough to express every firstord ..."
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Cited by 45 (4 self)
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Abstract. XPath 1.0 is a variable free language designed to specify paths between nodes in XML documents. Such paths can alternatively be specified in firstorder logic. The logical abstraction of XPath 1.0, usually called Navigational or Core XPath, is not powerful enough to express every firstorder definable path. In this paper we show that there exists a natural expansion of Core XPath in which every firstorder definable path in XML document trees is expressible. This expansion is called Conditional XPath. It contains additional axis relations of the form (child::n[F])+, denoting the transitive closure of the path expressed by child::n[F]. The difference with XPath’s descendant::n[F] is that the path (child::n[F])+ is conditional on the fact that all nodes in between should be labeled by n and should make the predicate F true. This result can be viewed as the XPath analogue of the expressive completeness of the relational algebra with respect to firstorder logic. 1
On Logics with Two Variables
 Theoretical Computer Science
, 1999
"... This paper is a survey and systematic presentation of decidability and complexity issues for modal and nonmodal twovariable logics. A classical result due to Mortimer says that the twovariable fragment of firstorder logic, denoted FO 2 , has the finite model property and is therefore decidable ..."
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Cited by 41 (8 self)
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This paper is a survey and systematic presentation of decidability and complexity issues for modal and nonmodal twovariable logics. A classical result due to Mortimer says that the twovariable fragment of firstorder logic, denoted FO 2 , has the finite model property and is therefore decidable for satisfiability. One of the reasons for the significance of this result is that many propositional modal logics can be embedded into FO 2 . Logics that are of interest for knowledge representation, for the specification and verification of concurrent systems and for other areas of computer science are often defined (or can be viewed) as extensions of modal logics by features like counting constructs, path quantifiers, transitive closure operators, least and greatest fixed points etc. Examples of such logics are computation tree logic CTL, the modal ¯calculus L¯ , or popular description logics used in artificial intelligence. Although the additional features are usually not firstorder...