David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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