A model-theoretic counterpart of loop formulas

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

68 Scopus citations

Abstract

In an important recent paper, Lin and Zhao introduced the concept of a loop formula, and showed that the answer sets for a logic program are exactly the models of Clark's completion of the program that satisfy the loop formulas. Just as supported sets are a model-theoretic account of completion, "externally supported" sets, defined in this paper, are a model-theoretic counterpart of loop formulas. This reformulation of loop formulas shows that they are related to assumption sets (Saccá and Zaniolo) and to unfounded sets (Van Gelder, Ross and Schlipf; Leone, Rullo and Scarcello), invented many years earlier. Other contributions of this paper includes a simplification of the definition of a loop, extending it to programs with classical negation and infinite programs, and a generalization of the definition of a loop formula.

Original languageEnglish (US)
Title of host publicationIJCAI International Joint Conference on Artificial Intelligence
Pages503-508
Number of pages6
StatePublished - 2005
Externally publishedYes
Event19th International Joint Conference on Artificial Intelligence, IJCAI 2005 - Edinburgh, United Kingdom
Duration: Jul 30 2005Aug 5 2005

Other

Other19th International Joint Conference on Artificial Intelligence, IJCAI 2005
CountryUnited Kingdom
CityEdinburgh
Period7/30/058/5/05

ASJC Scopus subject areas

  • Artificial Intelligence

Cite this

Lee, J. (2005). A model-theoretic counterpart of loop formulas. In IJCAI International Joint Conference on Artificial Intelligence (pp. 503-508)