David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
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 (2005). Gentzen-Type Methods for Bilattice Negation. Studia Logica 80 (2-3):265 - 289.
Arnon Avron (2005). A Non-Deterministic View on Non-Classical Negations. Studia Logica 80 (2-3):159 - 194.
Dimiter Vakarelov (2005). Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation. Studia Logica 80 (2-3):393-430.
Dimiter Vakarelov (2006). Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of Negation. Studia Logica 84 (1):105-127.
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