Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)

Some Categorical Equivalences for Nelson Algebras with Consistency Operators

Authors
Francesc Esteva, Aldo Figallo-Orellano, Tommaso Flaminio, Lluis Godo
Corresponding Author
Tommaso Flaminio
Available Online 30 August 2021.
DOI
https://doi.org/10.2991/asum.k.210827.056How to use a DOI?
Keywords
Nelson algebras, Heyting algebras, Consistency operators, Categorical equivalence
Abstract

The aim of this paper is to present categorical equivalences involving Nelson algebras with a consistency operator. These algebraic structures are the algebraic semantics of a paraconsistent logic, actually a logic of formal inconsistency, based on Nelson logic, also known as constructive logic with strong negation. In particular, we will extend a well-known relationship between Nelson algebras/lattices and Heyting algebras with a boolean filter to these expanded structures in terms of categorical equivalences.

Copyright
© 2021, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Cite this article

TY  - CONF
AU  - Francesc Esteva
AU  - Aldo Figallo-Orellano
AU  - Tommaso Flaminio
AU  - Lluis Godo
PY  - 2021
DA  - 2021/08/30
TI  - Some Categorical Equivalences for Nelson Algebras with Consistency Operators
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 420
EP  - 426
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.056
DO  - https://doi.org/10.2991/asum.k.210827.056
ID  - Esteva2021
ER  -