Studia Logica 105 (6):1167-1191 (2017)

Abstract
A classical paraconsistent logic, which is regarded as a modified extension of first-degree entailment logic, is introduced as a Gentzen-type sequent calculus. This logic can simulate the classical negation in classical logic by paraconsistent double negation in CP. Theorems for syntactically and semantically embedding CP into a Gentzen-type sequent calculus LK for classical logic and vice versa are proved. The cut-elimination and completeness theorems for CP are also shown using these embedding theorems. Similar results are also obtained for an intuitionistic paraconsistent logic, and several versions of Glivenko and Gödel-Gentzen translation theorems are proved for CP and IP.
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DOI 10.1007/s11225-017-9731-2
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References found in this work BETA

A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Constructible Falsity and Inexact Predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.

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