Abstract
Recently, the well-founded semantics of a logic programP has been strengthened to the well-founded semantics-by-case (WFC) and this in turn has been strengthened to the extended well-founded semantics (WFE). Both WFC(P) and WFE(P) have thelogical consequence property, namely, if an atomAj is true in the theory Th(P), thenAj is true in the semantics as well. However, neither WFC nor WFE has the GCWA property, i.e., if an atomAj is false in all minimal models ofP,Aj may not be false in WFC(P) (resp. WFE(P)). We extend the ideas in WFC and WFE to define a strong well-founded semantics WFS which has the GCWA property. The strong semantics WFS(P) is defined by combining GCWA with the notion ofderived rules. Here we use a new Type-III derived rules in addition to those used in WFC and WFE. The relationship between WFS and WFC is also clarified.
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