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Summer 1999 On Partial and Paraconsistent Logics
Reinhard Muskens
Notre Dame J. Formal Logic 40(3): 352-374 (Summer 1999). DOI: 10.1305/ndjfl/1022615616


In this paper we consider the theory of predicate logics in which the principle of bivalence or the principle of noncontradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove model existence. For $ \bf L_4$, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalize to partial and paraconsistent logics once the right setup is chosen. Our logic $ \bf L_4$ has a semantics that also underlies Belnap's logic and is related to the logic of bilattices. $ \bf L_4$ is in focus most of the time, but it is also shown how results obtained for $ \bf L_4$ can be transferred to several variants.


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Reinhard Muskens. "On Partial and Paraconsistent Logics." Notre Dame J. Formal Logic 40 (3) 352 - 374, Summer 1999.


Published: Summer 1999
First available in Project Euclid: 28 May 2002

zbMATH: 1007.03029
MathSciNet: MR1845625
Digital Object Identifier: 10.1305/ndjfl/1022615616

Primary: 03B53
Secondary: 03B60

Rights: Copyright © 1999 University of Notre Dame


Vol.40 • No. 3 • Summer 1999
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