Head-elementary-set-free logic programs

Authors:
Martin Gebser;Joohyung Lee;Yuliya Lierler
Affiliations:
Institut für Informatik, Universität Potsdam, Germany;School of Computing and Informatics, Arizona State University;Department of Computer Sciences, University of Texas at Austin
Venue:
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Year:
2007

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Abstract

The recently proposed notion of an elementary set yielded a refinement of the theorem on loop formulas, telling us that the stable models of a disjunctive logic program can be characterized by the loop formulas of its elementary sets. Based on the notion of an elementary set, we propose the notion of head-elementary-set-free (HEF) programs, a more general class of disjunctive programs than head-cycle-free (HCF) programs proposed by Ben-Eliyahu and Dechter, that can still be turned into nondisjunctive programs in polynomial time and space by "shifting" the head atoms into the body. We show several properties of HEF programs that generalize earlier results on HCF programs. Given an HEF program, we provide an algorithm for finding an elementary set whose loop formula is not satisfied, which has a potential for improving stable model computation by answer set solvers.