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An Algebraic Proof of the Admissibility of γ in Relevant Modal Logics

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Abstract

The admissibility of Ackermann’s rule γ is one of the most important problems in relevant logics. The admissibility of γ was first proved by an algebraic method. However, the development of Routley-Meyer semantics and metavaluational techniques makes it possible to prove the admissibility of γ using the method of normal models or the method using metavaluations, and the use of such methods is preferred. This paper discusses an algebraic proof of the admissibility of γ in relevant modal logics based on modern algebraic models.

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  1. University Evaluation Center, Headquarters for Strategy and Planning, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata City, 950-2181, Japan

    Takahiro Seki

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  1. Takahiro Seki
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Correspondence to Takahiro Seki.

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Seki, T. An Algebraic Proof of the Admissibility of γ in Relevant Modal Logics. Stud Logica 100, 1149–1174 (2012). https://doi.org/10.1007/s11225-012-9459-y

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