Super-\L ukasiewicz logics expanded by $\Delta$

TL;DR

This paper explores the extension of Super-ukiewicz logics with the Baaz elta operator, providing algebraic analysis, cardinality results, and an alternative axiomatization of the expanded logic.

Contribution

It introduces the elta operator into Super-ukiewicz logics, analyzes their algebraic structure, and offers a new axiomatization of the expanded logic.

Findings

Cardinality of Lindembaun-Tarski algebra with finite variables determined

Algebraic properties of elta in Super-ukiewicz logics analyzed

Alternative axiomatization of ukiewicz logic with elta provided

Abstract

Baaz's operator $\Delta$ 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 $\Delta$-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 $\Delta$ operator in the context of ($n$-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 $\Delta$.