On Partial and Paraconsistent Logics

Notre Dame Journal of Formal Logic 40 (3):352-374 (1999)
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In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, 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 generalise to partial and paraconsistent logics once the right set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s [4] and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants.

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Reinhard Muskens
University of Amsterdam

References found in this work

Situations and attitudes.Jon Barwise & John Perry - 1981 - Journal of Philosophy 78 (11):668-691.
Situations and Attitudes.Jon Barwise & John Perry - 1983 - Cambridge, Mass.: MIT Press. Edited by John Perry.
A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Toward useful type-free theories. I.Solomon Feferman - 1984 - Journal of Symbolic Logic 49 (1):75-111.

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