Modal extension of ideal paraconsistent four-valued logic and its subsystem

Annals of Pure and Applied Logic 171 (10):102830 (2020)

Abstract
This study aims to introduce a modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC as a Gentzen-type sequent calculus and prove the Kripke-completeness and cut-elimination theorems for M4CC. The logic M4CC is also shown to be decidable and embeddable into the normal modal logic S4. Furthermore, a subsystem of M4CC, which has some characteristic properties that do not hold for M4CC, is introduced and the Kripke-completeness and cut-elimination theorems for this subsystem are proved. This subsystem is also shown to be decidable and embeddable into S4.
Keywords Ideal paraconsistent four-valued logic  Gentzen-type sequent calculus  Kripke-completeness theorem  Cut-elimination theorem  Embedding theorem
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DOI 10.1016/j.apal.2020.102830
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