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63
Wellfounded semantics for description logic programs in the Semantic Web
, 2009
"... The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms, into a framework that is more useful for describing semantic content. In particular, combin ..."
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Cited by 71 (19 self)
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The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms, into a framework that is more useful for describing semantic content. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Nonmonotonic description logic programs (or dlprograms) were introduced for such a combination, in which a pair (L,P) of a description logic knowledge base L and a set of rules P with negation as failure is given a modelbased semantics that generalizes the answer set semantics of logic programs. In this paper, we reconsider dlprograms and present a wellfounded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the wellfounded semantics based on unfounded sets, and, as we show, lifts many of the wellknown properties from ordinary logic programs to dlprograms. Among these properties: our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dlprograms a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic
Answer Sets
, 2007
"... This chapter is an introduction to Answer Set Prolog a language for knowledge representation and reasoning based on the answer set/stable model semantics of logic programs [44, 45]. The language has roots in declarative programing [52, 65], the syntax and semantics of standard Prolog [24, 23], disj ..."
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Cited by 62 (5 self)
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This chapter is an introduction to Answer Set Prolog a language for knowledge representation and reasoning based on the answer set/stable model semantics of logic programs [44, 45]. The language has roots in declarative programing [52, 65], the syntax and semantics of standard Prolog [24, 23], disjunctive databases [66, 67] and nonmonotonic logic
Embedding NonGround Logic Programs into Autoepistemic Logic for Knowledge Base Combination
, 2008
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Answer sets for logic programs with arbitrary abstract constraint atoms
 J. ARTIFICIAL INTELLIGENCE RESEARCH
, 2007
"... In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (catoms). These approaches generalize the fixpointbased and the level mapping based answer set semantics of normal logic programs to the case of logic p ..."
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Cited by 29 (2 self)
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In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (catoms). These approaches generalize the fixpointbased and the level mapping based answer set semantics of normal logic programs to the case of logic programs with arbitrary types of catoms. The results are four different answer set definitions which are equivalent when applied to normal logic programs. The standard fixpointbased semantics of logic programs is generalized in two directions, called answer set by reduct and answer set by complement. These definitions, which differ from each other in the treatment of negationasfailure (naf) atoms, make use of an immediate consequence operator to perform answer set checking, whose definition relies on the notion of conditional satisfaction of catoms w.r.t. a pair of interpretations. The other two definitions, called strongly and weakly wellsupported models, are generalizations of the notion of wellsupported models of normal logic programs to the case of programs with catoms. As for the case of fixpointbased semantics, the difference between these two definitions is rooted in the treatment of naf atoms. We prove that answer sets by reduct (resp. by complement) are equivalent to weakly (resp. strongly) wellsupported models of a program, thus generalizing the theorem on the correspondence between stable models and wellsupported models of a normal logic program to the class of programs with catoms. We show that the newly defined semantics coincide with previously introduced semantics for logic programs with monotone catoms, and they extend the original answer set semantics of normal logic programs. We also study some properties of answer sets of programs with catoms, and relate our definitions to several semantics for logic programs with aggregates presented in the literature.
Logic programs with abstract constraint atoms
 In Proceedings of the 19th National Conference on Artificial Intelligence (AAAI04
, 2004
"... We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M, if M ∩ ..."
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Cited by 27 (6 self)
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We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M, if M ∩ X ∈ C. We focus here on monotone constraints, that is, those collections C that are closed under the superset. They include, in particular, weight (or pseudoboolean) constraints studied both by the logic programming and SAT communities. We show that key concepts of the theory of normal logic programs such as the onestep provability operator, the semantics of supported and stable models, as well as several of their properties including complexity results, can be lifted to such case.
Logic programs with abstract constraint atoms: the role of computations
 Proceedings of the 23rd International Conference on Logic Programming (ICLP 2007), LNCS, Springer, 2007 (this
, 2005
"... Abstract. We provide new perspectives on the semantics of logic programs with constraints. To this end we introduce several notions of computation and propose to use the results of computations as answer sets of programs with constraints. We discuss the rationale behind different classes of computat ..."
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Cited by 23 (3 self)
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Abstract. We provide new perspectives on the semantics of logic programs with constraints. To this end we introduce several notions of computation and propose to use the results of computations as answer sets of programs with constraints. We discuss the rationale behind different classes of computations and study the relationships among them and among the corresponding concepts of answer sets. The proposed semantics generalize the answer set semantics for programs with monotone, convex and/or arbitrary constraints described in the literature. 1
Managing uncertainty and vagueness in description logics, logic programs and description logic programs
, 2008
"... Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination). ..."
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Cited by 22 (6 self)
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Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination).
Properties and applications of programs with monotone and convex constraints
 J. ARTIFICIAL INTELLIGENCE RESEARCH
, 2006
"... We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop ..."
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Cited by 20 (0 self)
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We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop formulas. Our results provide an abstract account of properties of some recent extensions of logic programming with aggregates, especially the formalism of lparse programs. They imply a method to compute stable models of lparse programs by means of offtheshelf solvers of pseudoboolean constraints, which is often much faster than the smodels system.
Properties of programs with monotone and convex constraints
 In Proceedings of the 20th National Conference on Artificial Intelligence (AAAI05
, 2005
"... We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include tight programs and Fages Lemma, program completion and loop formulas, and the notions of strong and uniform equivalence with their char ..."
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Cited by 19 (4 self)
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We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include tight programs and Fages Lemma, program completion and loop formulas, and the notions of strong and uniform equivalence with their characterizations. Our results form an abstract account of properties of some recent extensions of logic programming with aggregates, especially the formalism of smodels.