Paraconsistent double negation as a modal operator

摘要

A paraconsistent modal-like logic, PM, is defined as a Gentzen-type sequent calculus. The modal operator in the modal logic S4 can be simulated by the paraconsistent double negation in PM. Some theorems for embedding PM into a Gentzen-type sequent calculus for S4 and vice versa are proved. The cut-elimination and completeness theorems for PM are also proved. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim