Well Founded Semantics for Logic Programs with Explicit Negation

The aim of this paper is to provide a semantics for general logic programs (with negation by default) extended with explicit negation, subsuming well founded semantics 22]. The Well Founded semantics for extended logic programs (WFSX) is expressible by a default theory semantics we have devised 11]. This relationship improves the cross{fertilization between logic programs and default theories, since we generalize previous results concerning their relationship 3, 4, 7, 1, 2], and there is an increasing use of logic programming with explicit negation for nonmonotonic reasoning 7, 15, 16, 13, 23]. It also clariies the meaning of logic programs combining both explicit negation and negation by default. In particular, it shows that explicit negation corresponds exactly to classical negation in the default theory, and elucidates the use of rules in logic programs. Like defaults, rules are unidirectional, so their contrapositives are not implicit; the rule connective , , is not material implication, but has rather the avour of an inference rule, like defaults. It is worth noting that existing top{down procedures for well-founded semantics without explicit negation 24, 14] can be easily adapted to the semantics we are proposing for extended programs. This issue is only brieey considered here and will be the subject of a forthcoming report.