Cyclic Negations and Four-valuedness
Logic in Computer Science
2022-04-15 v1
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.
Cite
@article{arxiv.2204.06733,
title = {Cyclic Negations and Four-valuedness},
author = {Oleg Grigoriev and Dmitry Zaitsev},
journal= {arXiv preprint arXiv:2204.06733},
year = {2022}
}
Comments
In Proceedings NCL 2022, arXiv:2204.06359