Super-\L ukasiewicz logics expanded by $\Delta$
Logic
2022-11-08 v1
Abstract
Baaz's operator was introduced (by Baaz) in order to extend G\"odel logics, after that this operator was used to expand fuzzy logics by H\'ajek in his celebrated book. These logics were called -fuzzy logics. On the other hand, possibility operators were studied in the setting of \L ukasiewicz-Moisil algebras; curiously, one of these operators coincide with the Baaz's one. In this paper, we study the operator in the context of (-valued) Super-\L ukasiewicz logics. An algebraic study of these logics is presented and the cardinality of Lindembaun-Tarski algebra with a finite number of variables is given. Finally, as a by-product, we present an alternative axiomatization of H\'ajek's \L ukasiwicz logic expanded with .
Cite
@article{arxiv.2211.02749,
title = {Super-\L ukasiewicz logics expanded by $\Delta$},
author = {Aldo V. Figallo and Aldo Figallo-Orellano and Martín Figallo},
journal= {arXiv preprint arXiv:2211.02749},
year = {2022}
}