Bipolarity in bilattice logics

✍ Scribed by Sébastien Konieczny; Pierre Marquis; Philippe Besnard

• Book ID: 102280104
• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 196 KB
• Volume: 23
• Category: Article
• ISSN: 0884-8173
• DOI: 10.1002/int.20306

✦ Synopsis

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.