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Characterizations of stable model semantics for logic programs with arbitrary constraint atoms

Published online by Cambridge University Press:  01 July 2009

YI-DONG SHEN ,
JIA-HUAI YOU  and
LI-YAN YUAN
YI-DONG SHEN
Affiliation:
State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China (e-mail: ydshen@ios.ac.cn)
JIA-HUAI YOU
Affiliation:
Department of Computing Science, University of Alberta, Edmonton, Alberta, T6G 2H1Canada (e-mail: you@cs.ualberta.ca, yuan@cs.ualberta.ca)
LI-YAN YUAN
Affiliation:
Department of Computing Science, University of Alberta, Edmonton, Alberta, T6G 2H1Canada (e-mail: you@cs.ualberta.ca, yuan@cs.ualberta.ca)
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Abstract

This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented compactly. We show two applications. First, under this representation of constraint atoms, we generalize the Gelfond–Lifschitz transformation and apply it to define stable models (also called answer sets) for logic programs with arbitrary constraint atoms. The resulting semantics turns out to coincide with the one defined by Son et al. (2007), which is based on a fixpoint approach. One advantage of our approach is that it can be applied, in a natural way, to define stable models for disjunctive logic programs with constraint atoms, which may appear in the disjunctive head as well as in the body of a rule. As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches. Second, we show that our abstract representation of constraint atoms provides a means to characterize dependencies of atoms in a program with constraint atoms, so that some standard characterizations and properties relying on these dependencies in the past for logic programs with ordinary atoms can be extended to logic programs with constraint atoms.

Keywords

answer set programingabstract constraint atomsstable model semanticsGelfond–Lifschitz transformation
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 9 , Issue 4 , July 2009 , pp. 529 - 564
Copyright
Copyright © Cambridge University Press 2009

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