On loop formulas with variables

Joohyung Lee, Yunsong Meng

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

18 Scopus citations

Abstract

Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary first-order sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop formulas to disjunctive programs and to arbitrary first-order sentences. We also extend the syntax of logic programs to allow explicit quantifiers, and define its semantics as a subclass of the new language of stable models by Ferraris et al. Such programs inherit from the general language the ability to handle nonmonotonic reasoning under the stable model semantics even in the absence of the unique name and the domain closure assumptions, while yielding more succinct loop formulas than the general language due to the restricted syntax. We also show certain syntactic conditions under which query answering for an extended program can be reduced to entailment checking in first-order logic, providing a way to apply first-order theorem provers to reasoning about non-Herbrand stable models.

Original languageEnglish (US)
Title of host publicationPrinciples of Knowledge Representation and Reasoning
Subtitle of host publicationProceedings of the 11th International Conference, KR 2008
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages444-453
Number of pages10
ISBN (Print)9781577353843
StatePublished - Jan 1 2008
Event11th International Conference on Principles of Knowledge Representation and Reasoning, KR 2008 - Sydney, NSW, Australia
Duration: Sep 16 2008Sep 19 2008

Publication series

NameProceedings of the International Workshop on Temporal Representation and Reasoning

Other

Other11th International Conference on Principles of Knowledge Representation and Reasoning, KR 2008
CountryAustralia
CitySydney, NSW
Period9/16/089/19/08

ASJC Scopus subject areas

  • Logic

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  • Cite this

    Lee, J., & Meng, Y. (2008). On loop formulas with variables. In Principles of Knowledge Representation and Reasoning: Proceedings of the 11th International Conference, KR 2008 (pp. 444-453). (Proceedings of the International Workshop on Temporal Representation and Reasoning). Institute of Electrical and Electronics Engineers Inc..