Three-Valued Semantics for Extended Logic Programs

In 4] , the semantics of monotonic (i.e. not-free) extended logic programs (ELPs) has been rephrased in three-valued logic for two purposes: achieving tractable reasoning with incomplete information and understanding the relationships between the existing semantics and many-valued logics. In this paper, we generalize this approach to unrestricted ELPs. We obtain a unifying view of many formalisms, including the answer set semantics, the well-founded semantics, generalized stable models (as in 11]), default logic, autoepistemic logic (AEL) and some of its variants (three-valued AEL and Schwartz's reeex-ive AEL). Our framework highlights surprising similarities between previously unrelated formalisms, such as TMS's with dependency directed backtracking, the WFSX semantics by Alferes and Pereira, and reeexive AEL. Moreover, we obtain very interesting new semantics, which make it possible to solve many hard benchmark problems with a substantial gain in elegance and eeciency.