David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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O. Arieli, A. Avron & A. Zamansky (2011). Ideal Paraconsistent Logics. Studia Logica 99 (1-3):31-60.
Norihiro Kamide & Heinrich Wansing (2011). Completeness and Cut-Elimination Theorems for Trilattice Logics. Annals of Pure and Applied Logic 162 (10):816-835.
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