On the extension of logic programming with negation through uniform proofs

Abstract. In the past, logic program semantics have been studied often separately from the underlying proof system, and this, consequently, leads to a somewhat confusing status of semantics. In this paper we show that elegant, yet natural semantics can be obtained by building a mechanism of justifying default assumptions on top of a proof system. In particular, we propose extended logic programming languages with negation through uniform proofs. The result is a very general framework, in which any abstract logic programming language can be extended to a nonmonotonic reasoning system, and many semantics, previously proposed and new, can be characterized and understood in terms of uniform proofs