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Hyperequivalence of Programs and Operators

Recent research in nonmonotonic logic programming has focused on different notions of program equivalence relevant for program optimization and modular programming. So far, most results concern the stable-model semantics. However, other semantics for logic programs are also of interest, especially the semantics of supported models which, when properly generalized, is closely related to a prominent nonmonotonic formalism, the autoepistemic logic of Moore. In this paper, we consider a framework of equivalence notions for logic programs under the supported (minimal) modelsemantics and provide characterizations for this framework in both model-theoretic and algebraic terms. We then use some of our results in order to obtain characterizations of the equivalence of theories in Moore’s autoepistemic logic.