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13
A new perspective on stable models
 In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI
, 2007
"... The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming (includi ..."
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Cited by 81 (35 self)
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The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming (including disjunctive rules, choice rules and conditional literals) and, unlike the original definition, refers neither to grounding nor to fixpoints. Rather, it is based on a syntactic transformation, which turns a logic program into a formula of secondorder logic that is similar to the formula familiar from the definition of circumscription. 1
Minimal logic programs
"... Abstract. bb We consider the problem of obtaining a minimal logic program strongly equivalent (under the stable models semantics) to a given arbitrary propositional theory. We propose a method consisting in the generation of the set of prime implicates of the original theory, starting from its set o ..."
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Cited by 10 (2 self)
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Abstract. bb We consider the problem of obtaining a minimal logic program strongly equivalent (under the stable models semantics) to a given arbitrary propositional theory. We propose a method consisting in the generation of the set of prime implicates of the original theory, starting from its set of countermodels (in the logic of HereandThere), in a similar vein to the QuineMcCluskey method for minimisation of boolean functions. As a side result, we also provide several results about fundamental rules (those that are not tautologies and do not contain redundant literals) which are combined to build the minimal programs. In particular, we characterise their form, their corresponding sets of countermodels, as well as necessary and sufficient conditions for entailment and equivalence among them.
Complexity results for answer set programming with bounded predicate arities and implications
, 2007
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Hyperequivalence of logic programs with respect to supported models
 PROCEEDINGS OF AAAI 2008
, 2008
"... Recent research in nonmonotonic logic programming has focused on certain types of program equivalence, which we refer to here as hyperequivalence, that are relevant for program optimization and modular programming. So far, most results concern hyperequivalence relative to the stablemodel semantics. ..."
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Cited by 7 (6 self)
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Recent research in nonmonotonic logic programming has focused on certain types of program equivalence, which we refer to here as hyperequivalence, that are relevant for program optimization and modular programming. So far, most results concern hyperequivalence relative to the stablemodel semantics. However, other semantics for logic programs are also of interest, especially the semantics of supported models which, when properly generalized, is closely related to the autoepistemic logic of Moore. In this paper, we consider a family of hyperequivalence relations for programs based on the semantics of supported and supported minimal models. We characterize these relations in modeltheoretic terms. We use the characterizations to derive complexity results concerning testing whether two programs are hyperequivalent relative to supported and supported minimal models.
Equivalences in answerset programming by countermodels in the logic of hereandthere
 of Lecture Notes in Computer Science
, 2008
"... Abstract. Different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in AnswerSet Programming, mainly for the purpose of identifying programs that can serve as substitutes without altering the semantics, for instance in program optimization. ..."
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Cited by 5 (3 self)
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Abstract. Different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in AnswerSet Programming, mainly for the purpose of identifying programs that can serve as substitutes without altering the semantics, for instance in program optimization. Such semantic comparisons are usually characterized by various selections of models in the logic of HereandThere (HT). For uniform equivalence however, correct characterizations in terms of HTmodels can only be obtained for finite theories, respectively programs. In this article, we show that a selection of countermodels in HT captures uniform equivalence also for infinite theories. This result is turned into coherent characterizations of the different notions of equivalence by countermodels, as well as by a mixture of HTmodels and countermodels (socalled equivalence interpretations). Moreover, we generalize the socalled notion of relativized hyperequivalence for programs to propositional theories, and apply the same methodology in order to obtain a semantic characterization which is amenable to infinite settings. This allows for a lifting of the results to firstorder theories under a very general semantics given in terms of a quantified version of HT. We thus obtain a general framework for the study of various notions of equivalence for theories under answerset semantics. Moreover, we prove an expedient property that allows for a simplified
A general framework for equivalences in answerset programming by countermodels in the logic of hereandthere. Theory and Practice of Logic Programming
, 2011
"... ar ..."
Minimising RDF Graphs under Rules and Constraints Revisited
, 2010
"... Based on practical observations on rulebased inference on RDF data, we study the problem of redundancy elimination in RDF in the presence of rules (in the form of Datalog rules) and constraints (in the form of socalled tuplegenerating dependencies). To this end, we investigate the influence of ..."
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Cited by 2 (1 self)
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Based on practical observations on rulebased inference on RDF data, we study the problem of redundancy elimination in RDF in the presence of rules (in the form of Datalog rules) and constraints (in the form of socalled tuplegenerating dependencies). To this end, we investigate the influence of several problem parameters (like restrictions on the size of the rules and/or the constraints) on the complexity of detecting redundancy. The main result of this paper is a finegrained complexity analysis of both graph and rule minimisation in various settings.
Redundancy Elimination on RDF Graphs in the Presence of Rules, Constraints, and Queries
"... Based on practical observations on rulebased inference on RDF data, we study the problem of redundancy elimination on RDF graphs in the presence of rules (in the form of Datalog rules) and constraints, (in the form of socalled tuplegenerating dependencies), and with respect to queries (ranging ..."
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Cited by 1 (0 self)
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Based on practical observations on rulebased inference on RDF data, we study the problem of redundancy elimination on RDF graphs in the presence of rules (in the form of Datalog rules) and constraints, (in the form of socalled tuplegenerating dependencies), and with respect to queries (ranging from conjunctive queries up to more complex ones, particularly covering features of SPARQL, such as union, negation, or filters). To this end, we investigate the influence of several problem parameters (like restrictions on the size of the rules, the constraints, and/or the queries) on the complexity of detecting redundancy. The main result of this paper is a finegrained complexity analysis of both graph and rule minimisation in various settings.
Minimal logic programs (extended report)
"... Abstract. aa We consider the problem of obtaining a minimal logic program strongly equivalent (under the stable models semantics) to a given arbitrary propositional theory. We propose a method consisting in the generation of the set of prime implicates of the original theory, starting from its set o ..."
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Abstract. aa We consider the problem of obtaining a minimal logic program strongly equivalent (under the stable models semantics) to a given arbitrary propositional theory. We propose a method consisting in the generation of the set of prime implicates of the original theory, starting from its set of countermodels (in the logic of HereandThere), in a similar vein to the QuineMcCluskey method for minimisation of boolean functions. As a side result, we also provide several results about fundamental rules (those that are not tautologies and do not contain redundant literals) which are combined to build the minimal programs. In particular, we characterise their form, their corresponding sets of countermodels, as well as necessary and sufficient conditions for entailment and equivalence among them.
Semantic Web 0 (0) 1 1
"... IOS Press Complexity of redundancy detection on RDF graphs in the presence of rules, constraints, and queries ..."
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IOS Press Complexity of redundancy detection on RDF graphs in the presence of rules, constraints, and queries