Basic Four-Valued Systems of Cyclic Negations

Authors

  • Oleg Grigoriev Lomonosov Moscow State University, Faculty of Philosophy, Department of Logic, 119234, Lomonosovskiy prospect 24, Building 4, Moscow, Russia image/svg+xml Author https://orcid.org/0000-0002-3984-3289
  • Dmitry Zaitsev Lomonosov Moscow State University, Faculty of Philosophy, Department of Logic, 119234, Lomonosovskiy prospect 24, Building 4, Moscow, Russia image/svg+xml Author

DOI:

https://doi.org/10.18778/0138-0680.2022.21

Keywords:

Generalized truth values, consequence relation, first degree entailment

Abstract

We consider an example of four valued semantics partially inspired by quantum computations and negation-like operations occurred therein. In particular we consider a representation of so called square root of negation within this four valued semantics as an operation which acts like a cycling negation. We define two variants of logical matrices performing different orders over the set of truth values. Purely formal logical result of our study consists in axiomatizing the logics of defined matrices as the systems of binary consequence relation and proving correctness and completeness theorems for these deductive systems.

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Published

2022-10-25

Issue

Vol. 51 No. 4 (2022)

Section

Research Article

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

Grigoriev, Oleg, and Dmitry Zaitsev. 2022. “Basic Four-Valued Systems of Cyclic Negations”. Bulletin of the Section of Logic 51 (4): 507-33. https://doi.org/10.18778/0138-0680.2022.21.
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