Strong and uniform equivalence of nonmonotonic theories – an algebraic approach

Abstract

We show that the concepts of strong and uniform equivalence of logic programs can be generalized to an abstract algebraic setting of operators on complete lattices. Our results imply characterizations of strong and uniform equivalence for several nonmonotonic logics including logic programming with aggregates, default logic and a version of autoepistemic logic.

Equilibrium logic

“…For it showed that while ordinary (answer set) equivalence is a computationally hard problem to check, strong equivalence amounts to the simpler (coNP-complete) problem of checking inter-derivability in a monotonic, multivalued logic. A spin-off of this result has been an effort to look more generally at strong equivalence in nonmonotonic logics and to see whether in other cases there may also exist computationally simpler, monotonic checks for strong equivalence, see eg [96,98] for the cases of default logic and causal theories, respectively, and [95] for a general framework applicable to different logics.…”

Hyperequivalence of logic programs with respect to supported models

“…The fact that most arguments in this paper have a strong algebraic flavor and thus may only loosely depend on specific syntactic features of logic programs adds further credibility to that contention. In our future work, we will aim to develop algebraic generalizations of the characterizations presented in this paper (algebraic generalizations of hyperequivalence under the stable-model semantics were developed in (Truszczynski 2006)), and we will study hyperequivalence in autoepistemic logic without imposing syntactic restrictions on formulas.…”

Guarded resolution for Answer Set Programming

“…We say that programs P , P are equivalent if Stab(P ) = Stab(P ). This notion and its strengthenings were studied by ASP community (Lifschitz, Pearce and Valverde 2001), (Truszczynski 2006). We have the following fact.…”