L.M.Pereira A model theory for paraconsistent logic programming

Abstract. We provide a nine-valued logic to characterize the models of logic programs under a paraconsistent well-founded semantics with explicit negation WFSX p. We define a truth-functional logic, NINE, based on the bilattice construction of Ginsberg and Fitting. The models identified by WFSX p are models of logic NINE. We conclude with a discussion on the conditions to obtain an isomorphism between the two definitions, and thereby characterizing WFSX p model-theoretically.