Negation-Free Definitions of Paraconsistency

Sankha S. Basu
(Indraprastha Institute of Information Technology - Delhi)
Sayantan Roy
(Indraprastha Institute of Information Technology - Delhi)

Paraconsistency is commonly defined and/or characterized as the failure of a principle of explosion. The various standard forms of explosion involve one or more logical operators or connectives, among which the negation operator is the most frequent. In this article, we ask whether a negation operator is essential for describing paraconsistency. In other words, is it possible to describe a notion of paraconsistency that is independent of connectives? We present two such notions of negation-free paraconsistency, one that is completely independent of connectives and another that uses a conjunction-like binary connective that we call 'fusion'. We also derive a notion of 'quasi-negation' from the former, and investigate its properties.

In Andrzej Indrzejczak and Michał Zawidzki: Proceedings of the 10th International Conference on Non-Classical Logics. Theory and Applications (NCL 2022), Łódź, Poland, 14-18 March 2022, Electronic Proceedings in Theoretical Computer Science 358, pp. 150–159.
Published: 14th April 2022.

ArXived at: https://dx.doi.org/10.4204/EPTCS.358.11 bibtex PDF
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