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.

Keywords

Natural deduction Post’s logic Post’s negation cyclic negation Dual Post’s logic many-valued logic proof theory 

Mathematics Subject Classification

Primary 03B50 Secondary 03B22 03F03 

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Notes

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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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Logic, Faculty of PhilosophyLomonosov Moscow State UniversityMoscowRussia

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