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On reductive semantics of aggregates in answer set programming
 In Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR
, 2009
"... Abstract. Several proposals of the semantics of aggregates are based on different extensions of the stable model semantics, which makes it difficult to compare them. In this note, building upon a reductive approach to designing aggregates, we provide reformulations of some existing semantics in term ..."
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Abstract. Several proposals of the semantics of aggregates are based on different extensions of the stable model semantics, which makes it difficult to compare them. In this note, building upon a reductive approach to designing aggregates, we provide reformulations of some existing semantics in terms of propositional formulas, which help us compare the semantics and understand their properties in terms of their propositional formula representations. We also present a generalization of semantics of aggregates without involving grounding, and define loop formulas for programs with aggregates guided by the reductive approach. 1
178 Stable Model Semantics and FirstOrder Loop Formulas
 In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI
, 2005
"... Lin and Zhao’s theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the firstorder case. We investigate the precise relationship betwe ..."
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Cited by 4 (1 self)
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Lin and Zhao’s theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the firstorder case. We investigate the precise relationship between the firstorder stable model semantics and firstorder loop formulas, and study conditions under which the former can be represented by the latter. In order to facilitate the comparison, we extend the definition of a firstorder loop formula which was limited to a nondisjunctive program, to a disjunctive program and to an arbitrary firstorder theory. Based on the studied relationship we extend the syntax of a logic program with explicit quantifiers, which allows us to do reasoning involving nonHerbrand stable models using firstorder reasoners. Such programs can be viewed as a special class of firstorder theories under the stable model semantics, which yields more succinct loop formulas than the general language due to their restricted syntax. 1.
Weight Constraint Programs with Functions
"... Abstract. In this paper we consider a new class of logic programs, called weight constraint programs with functions, which are lparse programs incorporating functions over nonHerbrand domains. We define answer sets for these programs and develop a computational mechanism based on loop completion. W ..."
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Abstract. In this paper we consider a new class of logic programs, called weight constraint programs with functions, which are lparse programs incorporating functions over nonHerbrand domains. We define answer sets for these programs and develop a computational mechanism based on loop completion. We present our results in two stages. First, we formulate loop formulas for lparse programs (without functions). Our result improves the previous formulations in that our loop formulas do not introduce new propositional variables, nor there is a need of translating lparse programs to nested expressions. Building upon this result we extend the work to weight constraint programs with functions. We show that the loop completion of such a program can be transformed to a Constraint Satisfaction Problem (CSP) whose solutions correspond to the answer sets of the program, hence offtheshelf CSP solvers can be used for answer set computation. We show some preliminary experimental results. 1
Under consideration for publication in Theory and Practice of Logic Programming 1 Multithreaded ASP Solving with clasp
"... submitted [n/a]; revised [n/a]; accepted [n/a] We present the new multithreaded version of the stateoftheart answer set solver clasp. We detail its component and communication architecture and illustrate how they support the principal functionalities of clasp. Also, we provide some insights into ..."
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submitted [n/a]; revised [n/a]; accepted [n/a] We present the new multithreaded version of the stateoftheart answer set solver clasp. We detail its component and communication architecture and illustrate how they support the principal functionalities of clasp. Also, we provide some insights into the data representation used for different constraint types handled by clasp. All this is accompanied by an extensive experimental analysis of the major features related to multithreading in clasp. 1
Under consideration for publication in Theory and Practice of Logic Programming 1 Computing Loops with at Most One External Support Rule for Basic Logic Programs with Arbitrary Constraint Atoms
, 2003
"... The wellfounded semantics of logic programs is not only an important semantics but also serves as an essential tool for program simplification in answer set computations. Recently, it has been shown that for normal and disjunctive programs, the wellfounded models can be computed by unit propagatio ..."
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The wellfounded semantics of logic programs is not only an important semantics but also serves as an essential tool for program simplification in answer set computations. Recently, it has been shown that for normal and disjunctive programs, the wellfounded models can be computed by unit propagation on program completion and loop formulas of loops with no external support. An attractive feature of this approach is that when loop formulas of loops with exactly one external support are added, consequences beyond the wellfounded model can be computed, which sometimes can significantly speed up answer set computation. In this paper, we extend this approach to basic logic programs with abstract constraint atoms. We define program completion and loop formulas and show how to capture the wellfounded semantics that approximate answer sets of basic logic programs. We show that by adding the loop formulas of loops with one external support, consequences beyond wellfounded models can be computed. Our experiments show that for certain logic programs with constraints accepted by lparse, the consequences computed by our algorithms can speed up current ASP solvers smodels and clasp.
1 Under consideration for publication in Theory and Practice of Logic Programming 1 On Elementary Loops of Logic Programs
, 2010
"... ar ..."
Under consideration for publication in Theory and Practice of Logic Programming 1 On Elementary Loops of Logic Programs
, 2010
"... Part of the Computer Sciences Commons This Article is brought to you for free and open access by the Department of Computer Science at ..."
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Part of the Computer Sciences Commons This Article is brought to you for free and open access by the Department of Computer Science at
Strong Equivalence of Logic Programs with Abstract Constraint Atoms
"... Abstract. Logic programs with abstract constraint atoms provide a unifying framework for studying logic programs with various kinds of constraints. Establishing strong equivalence between logic programs is a key property for program maintenance and optimization, and for guaranteeing the same behavi ..."
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Abstract. Logic programs with abstract constraint atoms provide a unifying framework for studying logic programs with various kinds of constraints. Establishing strong equivalence between logic programs is a key property for program maintenance and optimization, and for guaranteeing the same behavior for a revised original program in any context. In this paper, we study strong equivalence of logic programs with abstract constraint atoms. We first give a general characterization of strong equivalence based on a new definition of program reduct for logic programs with abstract constraints. Then we consider a particular kind of program revisionconstraint replacements addressing the question: under what conditions can a constraint in a program be replaced by other constraints, so that the resulting program is strongly equivalent to the original one.