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Gentzen-type formulation of the prepositional logic LQ

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Abstract

We give a Gentzen-type formulation GQ for the intermediate logic LQ and prove the cut-elimination theorem on it, where LQ is the propositional logic obtained from the intuitionistic propositional logic LI by adding the axioms of the form ℸ AV ℸℸ A.

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References

  1. B. R. Boričić, A cut-free Gentzen-type system for the logic of the weak law of excluded middle, Studia Logica 45 (1986), pp. 39–53.

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Authors and Affiliations

  1. Department of Information Sciences, Science University of Tokyo, Noda City, 278, Chiba, Japan

    Tsutomu Hosoi

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  1. Tsutomu Hosoi
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Hosoi, T. Gentzen-type formulation of the prepositional logic LQ . Stud Logica 47, 41–48 (1988). https://doi.org/10.1007/BF00374051

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  • DOI: https://doi.org/10.1007/BF00374051

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