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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.