Elementary sets for logic programs

Martin Gebser, Joohyung Lee, Yuliya Lierler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Scopus citations

Abstract

By introducing the concepts of a loop and a loop formula, Lin and Zhao showed that the answer sets of a nondisjunctive logic program are exactly the models of its Clark's completion that satisfy the loop formulas of all loops. Recently, Gebser and Schaub showed that the Lin-Zhao theorem remains correct even if we restrict loop formulas to a special class of loops called "elementary loops." In this paper, we simplify and generalize the notion of an elementary loop, and clarify its role. We propose the notion of an elementary set, which is almost equivalent to the notion of an elementary loop for nondisjunctive programs, but is simpler, and, unlike elementary loops, can be extended to disjunctive programs without producing unintuitive results. We show that the maximal unfounded elementary sets for the "relevant" part of a program are exactly the minimal sets among the nonempty unfounded sets. We also present a graph-theoretic characterization of elementary sets for nondisjunctive programs, which is simpler than the one proposed in (Gebser & Schaub 2005). Unlike the case of nondisjunctive programs, we show that the problem of deciding an elementary set is coNP-complete for disjunctive programs.

Original languageEnglish (US)
Title of host publicationProceedings of the 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06
Pages244-249
Number of pages6
StatePublished - Nov 13 2006
Event21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06 - Boston, MA, United States
Duration: Jul 16 2006Jul 20 2006

Publication series

NameProceedings of the National Conference on Artificial Intelligence
Volume1

Other

Other21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06
CountryUnited States
CityBoston, MA
Period7/16/067/20/06

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence

Cite this

Gebser, M., Lee, J., & Lierler, Y. (2006). Elementary sets for logic programs. In Proceedings of the 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06 (pp. 244-249). (Proceedings of the National Conference on Artificial Intelligence; Vol. 1).