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The simple substitution property of Gödel's intermediate propositional logics S n 's

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Abstract

The simple substitution property provides a systematic and easy method for proving a theorem from the additional axioms of intermediate prepositional logics. There have been known only four intermediate logics that have the additional axioms with the property. In this paper, we reformulate the many valued logics S' n defined in Gödel [3] and prove the simple substitution property for them. In our former paper [9], we proved that the sets of axioms composed of one prepositional variable do not have the property except two of them. Here we provide another proof for this theorem.

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

    Katsumi Sasaki

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  1. Katsumi Sasaki
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Sasaki, K. The simple substitution property of Gödel's intermediate propositional logics S n 's. Studia Logica 49, 471–481 (1990). https://doi.org/10.1007/BF00370159

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  • DOI: https://doi.org/10.1007/BF00370159

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