A decidable paraconsistent relevant logic: Gentzen system and Routley‐Meyer semantics | Zendy

Kamide Norihiro | Zendy

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A decidable paraconsistent relevant logic: Gentzen system and Routley‐Meyer semantics

Author(s) -

Kamide Norihiro

Publication year - 2016

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.201400086

Subject(s) - mathematics , paraconsistent logic , decidability , negation , sequent calculus , intuitionistic logic , discrete mathematics , property (philosophy) , calculus (dental) , higher order logic , propositional calculus , programming language , computer science , description logic , mathematical proof , philosophy , epistemology , medicine , dentistry , geometry

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.

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