Logic programs with abstract constraint atoms: The role of computations

Authors:
Lengning Liu;Enrico Pontelli;Tran Cao Son;Miroslaw Truszczyński
Affiliations:
Department of Computer Science, University of Kentucky, Lexington, KY 40506, USA;Department of Computer Science, New Mexico State University, Las Cruces, NM 88003, USA;Department of Computer Science, New Mexico State University, Las Cruces, NM 88003, USA;Department of Computer Science, University of Kentucky, Lexington, KY 40506, USA
Venue:
Artificial Intelligence
Year:
2010

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Abstract

We provide a new perspective on the semantics of logic programs with arbitrary abstract constraints. To this end, we introduce several notions of computation. We use the results of computations to specify answer sets of programs with constraints. We present the rationale behind the classes of computations we consider, and discuss the relationships among them. We also discuss the relationships among the corresponding concepts of answer sets. One of those concepts has several compelling characterizations and properties, and we propose it as the correct generalization of the answer-set semantics to the case of programs with arbitrary constraints. We show that several other notions of an answer set proposed in the literature for programs with constraints can be obtained within our framework as the results of appropriately selected classes of computations.