Characterization of strongly equivalent logic programs in intermediate logics

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 Godel 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 -A boolean OR -A to intuitionistic logic), is the weakest intermediate logic for which strongly equivalent logic programs, in a language allowing negations, are logically equivalent.