Kripke-Completeness and Cut-elimination Theorems for Intuitionistic Paradefinite Logics With and Without Quasi-Explosion

Journal of Philosophical Logic:1-28 (forthcoming)

Abstract
Two intuitionistic paradefinite logics N4C and N4C+ are introduced as Gentzen-type sequent calculi. These logics are regarded as a combination of Nelson’s paraconsistent four-valued logic N4 and Wansing’s basic constructive connexive logic C. The proposed logics are also regarded as intuitionistic variants of Arieli, Avron, and Zamansky’s ideal paraconistent four-valued logic 4CC. The logic N4C has no quasi-explosion axiom that represents a relationship between conflation and paraconsistent negation, but the logic N4C+ has this axiom. The Kripke-completeness and cut-elimination theorems for N4C and N4C+ are proved.
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DOI 10.1007/s10992-020-09553-w
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