Terms that define nuclei on residuated lattices: a case study of BL-algebras
Logic
2024-12-30 v1
Abstract
A nucleus on a (bounded commutative integral) residuated lattice is a closure operator that satisfies the inequality for all . In this article, among several results, a description of an arbitrary nucleus on a residuated lattice is given. Special attention is given to terms that define a nucleus on every structure of a variety, as a means of generalizing the double negation operation. Some general results about these terms are presented, together with examples. The main result of this article consists of the description of all terms of this kind for every given subvariety of BL-algebras. We exhibit interesting nontrivial examples.
Cite
@article{arxiv.2412.19690,
title = {Terms that define nuclei on residuated lattices: a case study of BL-algebras},
author = {Sebastián Buss and Diego Castaño and José Patricio Díaz Varela},
journal= {arXiv preprint arXiv:2412.19690},
year = {2024}
}