A Hierarchy of Weak Double Negations |
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Authors: | Norihiro Kamide |
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Affiliation: | 1. Faculty of Information Technology and Business, Cyber University, 4F, 1-11 Kitayamabushi-cho, Shinjuku-ku, Tokyo, 162-0853, Japan
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Abstract: | In this paper, a way of constructing many-valued paraconsistent logics with weak double negation axioms is proposed. A hierarchy of weak double negation axioms is addressed in this way. The many-valued paraconsistent logics constructed are defined as Gentzen-type sequent calculi. The completeness and cut-elimination theorems for these logics are proved in a uniform way. The logics constructed are also shown to be decidable. |
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