Integrating the Completion and the Well Founded Semantics

The three most well-known semantics for negation in the logic programming framework are Clark's completion [Cla78], the stable semantics [GL88], and the well-founded semantics [vGRS91]. Clark's completion (COMP) was the first proposal to give a formal meaning to negation as failure. However, it is now accepted that COMP does not always captures the meaning of a logic program. Despite its computational and structural advantages, the well-founded semantics (WFS) is considered much too weak for real applications. The stable semantics (STABLE), on the other hand, is so strong that many programs become inconsistent. We present in this paper examples to support these claims, and we introduce a new semantics, called CWFS, which is as powerful as COMP in inferring positive literals and as powerful as WFS in inferring negative literals. Due to its particular construction, CWFS helps to understand the relationship among COMP, WFS, and STABLE. We also discuss some implementation issues of CWFS.