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A Hierarchy of Weak Double Negations

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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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Authors and Affiliations

  1. Faculty of Information Technology and Business, Cyber University, 4F, 1-11 Kitayamabushi-cho, Shinjuku-ku, Tokyo, 162-0853, Japan

    Norihiro Kamide

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  1. Norihiro Kamide
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Correspondence to Norihiro Kamide.

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Kamide, N. A Hierarchy of Weak Double Negations. Stud Logica 101, 1277–1297 (2013). https://doi.org/10.1007/s11225-013-9533-0

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