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

Thomas Eiter, Michael Fink, Hans Tompits, Stefan Woltran

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.