On the relations between stable and well-founded semantics of logic programs

Abstract

We study the relations between stable and well-founded semantics of logic programs. 1. We show that stable semantics can be defined in the same way as well-founded semantics based on the basic notion of unfounded sets. Hence, stable semantics can be considered as “two-valued well-founded semantics”. 2. An axiomatic characterization of stable and well-founded semantics of logic programs is given by a new completion theory, called strong completion. Similar to the Clark's completion, the strong completion can be interpreted in either two-valued or three-valued logic. We show that ◦ Two-valued strong completion specifies the stable semantics. ◦ Three-valued strong completion specifies the well-founded semantics. 3. We study the equivalence between stable semantics and well-founded semantics. At first, we prove the equivalence between the two semantics for strict programs. Then we introduce the bottom-stratified and top-strict condition generalizing both the stratifiability and the strictness, and show that the new condition is sufficient for the equivalence between stable and well-founded semantics. Further, we show that the call-consistency condition is sufficient for the existence of at least one stable model.