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Characterization of strongly equivalent logic programs in intermediate logics

Published online by Cambridge University Press:  13 May 2003

DICK H. J. DE JONGH  and
LEX HENDRIKS
DICK H. J. DE JONGH
Affiliation:
Institute of Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands (email: dickdj@science.uva.nl)
LEX HENDRIKS
Affiliation:
Institute of Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands (email: lhendrik@science.uva.nl)
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Abstract

The non-classical, nonmonotonic inference relation associated with the answer set semantics for logic programs gives rise to a relationship of strong equivalence between logical programs that can be verified in 3-valued Gödel logic, G3, the strongest non-classical intermediate propositional logic (Lifschitz et al., 2001). In this paper we will show that KC (the logic obtained by adding axiom $\neg A\vee\neg\neg A$ to intuitionistic logic), is the weakest intermediate logic for which strongly equivalent logic programs, in a language allowing negations, are logically equivalent.

Keywords

answer set semanticsstrongly equivalent programspropositional intermediate logics
Type
Research Article
Information
Theory and Practice of Logic Programming , Volume 3 , Issue 3 , May 2003 , pp. 259 - 270
Copyright
© 2003 Cambridge University Press

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