Super-Łukasiewicz logics expanded by Δ

Baaz's operator Δ was introduced (by Baaz) in order to extend Gödel logics, after that this operator was used to expand fuzzy logics by Hájek in his celebrated book. These logics were called Δ-fuzzy logics. On the other hand, possibility operators were studied in the setting of Łukasiewicz-Mois...

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Bibliographic Details
Published in:Fuzzy sets and systems 2023-08, Vol.465, p.108549, Article 108549
Main Authors: Figallo, A.V., Figallo-Orellano, A., Figallo, M.
Format: Article
Language:English
Subjects:
Baaz's operator
Free algebras
Super Łukasiewicz logics
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Summary:Baaz's operator Δ was introduced (by Baaz) in order to extend Gödel logics, after that this operator was used to expand fuzzy logics by Hájek in his celebrated book. These logics were called Δ-fuzzy logics. On the other hand, possibility operators were studied in the setting of Łukasiewicz-Moisil algebras; curiously, one of these operators coincide with the Baaz's one. In this paper, we study the Δ operator in the context of (n-valued) Super-Łukasiewicz 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 Hájek's Łukasiwicz logic expanded with Δ.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2023.108549