Strong and Uniform Equivalence in Answer-Set Programming: Characterizations and Complexity Results for the Non-Ground Case

Abstract

Recent research in nonmonotonic logic programming under the answer-set semantics studies different notions of equivalence. In particular, strong and uniform equivalence are proposed as useful tools for optimizing (parts of) a logic program. While previous research mainly addressed propositional (i.e., ground) programs, we deal here with the more general case of non-ground programs, and provide semantical characterizations capturing the essence of equivalence, generalizing the concepts of SE-models and UE-models, respectively, as originally introduced for propositional programs. We show that uniform equivalence is undecidable, and we give decidability results and precise complexity bounds for strong equivalence (thereby correcting a previous complexity bound for strong equivalence from the literature) as well as for uniform equivalence for finite vocabularies.

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Cite this paper

@inproceedings{Eiter2005StrongAU, title={Strong and Uniform Equivalence in Answer-Set Programming: Characterizations and Complexity Results for the Non-Ground Case}, author={Thomas Eiter and Michael Fink and Hans Tompits and Stefan Woltran}, booktitle={AAAI}, year={2005} }