A decidable paraconsistent relevant logic: Gentzen system and Routley‐Meyer semantics |
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Authors: | Norihiro Kamide |
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Institution: | Department of Information and Electronic Engineering, Faculty of Science and Engineering, Teikyo University, Utsunomiya, Tochigi, Japan |
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Abstract: | In this paper, the positive fragment of the logic 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 . This extended relevant logic is called , and it has the property of constructible falsity which is known to be a characteristic property of . A Gentzen‐type sequent calculus for is introduced, and the cut‐elimination and decidability theorems for are proved. Two extended Routley‐Meyer semantics are introduced for , and the completeness theorems with respect to these semantics are proved. |
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