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Natural Deduction for Post’s Logics and their Duals

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Abstract

In this paper, we introduce the notion of dual Post’s negation and an infinite class of Dual Post’s finitely-valued logics which differ from Post’s ones with respect to the definitions of negation and the sets of designated truth values. We present adequate natural deduction systems for all Post’s k-valued (\(k\geqslant 3\)) logics as well as for all Dual Post’s k-valued logics.

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Acknowledgements

My special thanks go to Dmitry Zaitsev, Andrzej Pietruszczak, and Mateusz Klonowski. I also extend my thanks to an anonymous referee for valuable remarks.

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  1. Department of Logic, Faculty of Philosophy, Lomonosov Moscow State University, Lomonosovsky prospekt 27-4, Moscow, Russia, 119991

    Yaroslav Petrukhin

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  1. Yaroslav Petrukhin
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Correspondence to Yaroslav Petrukhin.

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To Sabrina Skoryukina

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Petrukhin, Y. Natural Deduction for Post’s Logics and their Duals. Log. Univers. 12, 83–100 (2018). https://doi.org/10.1007/s11787-018-0190-y

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