Bilattices and the semantics of logic programming

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Abstract

Bilattices, due to M. Ginsberg, are a family of truth-value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap's four-valued logic, based on classical two-valued logic. Among other examples are those based on finite many-valued logics and on probabilistic-valued logic. A fixed-point semantics is developed for logic programming, allowing any bilattice as the space of truth values. The mathematics is little more complex than in the classical two-valued setting, but the result provides a natural semantics for distributed logic programs, including those involving confidence factors. The classical two-valued and the Kripke-Kleene three-valued semantics become special cases, since the logics involved are natural sublogics of Belnap's logic, the logic given by the simplest bilattice.

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Research partly supported by NSF Grant CCR-8702307 and PSC-CUNY Grant 6-67295.