Combining Explicit Negation and Negation by Failure Via Belnap's Logic

This paper deals with logic programs containing two kinds of negation: negation as failure and explicit negation. This allows two diierent forms of reasoning in the presence of incomplete information. Such programs have been introduced by Gelfond and Lifschitz and called extended programs. We provide them with a logical semantics in the style of Kunen, based on Belnap's four-valued logic, and an answer sets' semantics that is shown to be equivalent to that of Gelfond and Lifschitz. The proofs rely on a translation into normal programs, and on a variant of Fit-ting's extension of logic programming to bilattices.