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.