A decidable paraconsistent relevant logic: Gentzen system and Routley‐Meyer semantics. Issue 3 (2nd May 2016)

• Record Type: Journal Article
• Authors: Kamide, Norihiro
• Is Part Of: Mathematical logic quarterly. Volume 62:Issue 3(2016)
• Page Start: 177
• Page End: 189
• Publication Date: 2016-05-02
• Subjects: Mathematics -- Periodicals; Logic, Symbolic and mathematical -- Periodicals; 511.3
• DOI: 10.1002/malq.201400086
• Languages: English
• ISSNs: 0942-5616

Abstract

Abstract : In this paper, the positive fragment of the logic RW of contraction‐less relevant implication is extended with the addition of a paraconsistent negation connective similar to the strong negation connective in Nelson's paraconsistent four‐valued logic N 4 . This extended relevant logic is called RWP, and it has the property of constructible falsity which is known to be a characteristic property of N 4 . A Gentzen‐type sequent calculus SRWP for RWP is introduced, and the cut‐elimination and decidability theorems for SRWP are proved. Two extended Routley‐Meyer semantics are introduced for RWP, and the completeness theorems with respect to these semantics are proved.