Notre Dame Journal of Formal Logic

On Partial and Paraconsistent Logics

Reinhard Muskens


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.

Article information

Notre Dame J. Formal Logic, Volume 40, Number 3 (1999), 352-374.

First available in Project Euclid: 28 May 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B53: Paraconsistent logics
Secondary: 03B60: Other nonclassical logic


Muskens, Reinhard. On Partial and Paraconsistent Logics. Notre Dame J. Formal Logic 40 (1999), no. 3, 352--374. doi:10.1305/ndjfl/1022615616.

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