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The method of axiomatic rejection for the intuitionistic propositional logic

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Abstract

We prove that the intuitionistic sentential calculus is Ł-decidable (decidable in the sense of Łukasiewicz), i.e. the sets of theses of Int and of rejected formulas are disjoint and their union is equal to all formulas. A formula is rejected iff it is a sentential variable or is obtained from other formulas by means of three rejection rules. One of the rules is original, the remaining two are Łukasiewicz's rejection rules: by detachement and by substitution. We extensively use the method of Beth's semantic tableaux.

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Authors and Affiliations

  1. Department of Logic and Methodology of Sciences, WrocŁaw University, ul. Szewska 36, 50-139, WrocŁaw

    Rafal Dutkiewicz

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  1. Rafal Dutkiewicz
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To the memory of Jerzy Słupecki

Translated from the Polish by Jan Zygmunt. Preparation of this paper was supported in part by C.P.B.P. 08-15.

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Dutkiewicz, R. The method of axiomatic rejection for the intuitionistic propositional logic. Studia Logica 48, 449–459 (1989). https://doi.org/10.1007/BF00370199

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  • DOI: https://doi.org/10.1007/BF00370199

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