Topological model set deformations in logic programming

Aida Batarekh*, V. S. Subrahmanian

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

Given a first order language, and a notion of a logic L w.r.t. the language, we investigate the topological properties of the space of L-structures for the language. We show that under a topology called the query topology which arises naturally in logic programming, the space of L-models (where L is a decent logic) of any sentence (set of clauses) in the language may be regarded as a (closed, compact) T4-space. We then investigate the properties of maps from structures to structures. Our results allow us to apply various well-known results on the fixed-points of operators on topological spaces to the semantics of logic programming -in particular, we are able to derive necessary and sufficient topological conditions for the completion of covered general logic programs to be consistent. Moreover, we derive sufficient conditions guaranteeing the consistency of program completions, and for logic programs to be determinate. We also apply our results to characterize consistency of the unions of program completions.

Original languageEnglish (US)
Pages (from-to)357-399
Number of pages43
JournalFundamenta Mathematicae
Volume12
Issue number3
StatePublished - Sep 1989
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory

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