Well-Founded Semantics, Generalized


Classical fixpoint semantics for logic programs is based on the TP immediate consequence operator. The Kripke/Kleene, three-valued, semantics uses ΦP, which extends TP to Kleene’s strong three-valued logic. Both these approaches generalize to cover logic programming systems based on a wide class of logics, provided only that the underlying structure be that of a bilattice. This was presented in earlier papers. Recently well-founded semantics has become influential for classical logic programs. We show how the well-founded approach also extends naturally to the same family of bilatticebased programming languages that the earlier fixpoint approaches extended to. Doing so provides a natural semantics for logic programming systems that have already been proposed, as well as for a large number that are of only theoretical interest. And finally, doing so simplifies the proofs of basic results about the well-founded semantics, by stripping away inessential details.



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Melvin Fitting
CUNY Graduate Center

References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Truth and reflection.Stephen Yablo - 1985 - Journal of Philosophical Logic 14 (3):297 - 349.
The Stable Model Semantics for Logic Programming.Melvin Fitting - 1992 - Journal of Symbolic Logic 57 (1):274-277.

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