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 Gödel 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 $\neg A\vee\neg\neg A$ to intuitionistic logic), is the weakest intermediate logic for which strongly equivalent logic programs, in a language allowing negations, are logically equivalent.