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Theories of Propositional Logics and the Converse of Substitution

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Abstract

The question of the existence and the number of substitutional logics is considered. Every tabular logic with a functionally complete system of connectives is proved to be substitutional. For these logics, the existence of an algorithm is proved, which uses calculable consistent axiomatics of the theory to construct an exact unifying substitution for it. A denumerable number of substitutional tabular logics is constructed. Some substitutional tabular logics with meaningful interpretation are presented. Moreover, every substitutional logic is proved to have a characteristic matrix. The set of nonsubstitutional logics is proved to be continual.

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Funding

This work is supported by the Russian Scientific Foundation (grant no. 21-18-00195).

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Authors and Affiliations

  1. Tver State University, 170100, Tver, Russia

    I. A. Gorbunov

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  1. I. A. Gorbunov
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Correspondence to I. A. Gorbunov.

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The authors declare that they have no conflicts of interest.

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Translated by M. Talacheva

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Gorbunov, I.A. Theories of Propositional Logics and the Converse of Substitution. Russ Math. 66, 26–32 (2022). https://doi.org/10.3103/S1066369X22050048

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  • DOI: https://doi.org/10.3103/S1066369X22050048

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