Bipolarity in bilattice logics

Authors:
Sébastien Konieczny;Pierre Marquis;Philippe Besnard
Affiliations:
CRIL UMR CNRS 8188, Université Lille-Nord de France, Artois, Lens, France;CRIL UMR CNRS 8188, Université Lille-Nord de France, Artois, Lens, France;IRIT UMR CNRS 5155, Université Paul Sabatier, Toulouse, France
Venue:
International Journal of Intelligent Systems - Bipolar Representations of Information and Preference Part 2: Reasoning and Learning
Year:
2008

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Abstract

This paper is centered on a family of propositional multivalued logics, based on bilattices. The semantics of such logics relies on a set of “truth values,” with two orderings that give the set a bilattice structure. Many interesting inference relations can be defined on these grounds, especially paraconsistent ones and-or nonmonotonic ones. The focus is laid on Belnap's fundamental bilattice logic FOUR, with four “epistemic truth values,” which proves sufficient for the purpose of inference. We show how the bilattice can be associated with a second biordinal structure, which no longer is bilatticial but bipolar. We show how additional inference relations in the logic FOUR can be obtained by exploiting the two preorders associated with this structure. © 2008 Wiley Periodicals, Inc.