The \(L\Pi\) and \(L\Pi\frac 12\) logics: Two complete fuzzy systems joining Łukasiewicz and product logics. (English) Zbl 0966.03022

Esteva, Francesc; Godo, Lluís; Montagna, Franco

Arch. Math. Logic 40, No. 1, 39-67 (2001).

The authors of this very interesting paper give a finite axiomatization for constructing two logics, called \(L \Pi\) and \(L\Pi {1 \over 2} \). Completeness results are given by means of the algebras associated to these logics, and a subdirect representation theorem for them is proved. While \( L \Pi\) results from a combination of Lukasiewicz and Product Logic, \(L\Pi {1 \over 2} \) happens to contain the most important propositional fuzzy logics: Lukasiewicz and Product Logic, Gödel’s Fuzzy Logic, Takeuti and Titani’s Propositional Logic, Pavelka’s Rational and Product Logic, etc. Some nice particular results are studied.

Reviewer: Claudi Alsina (Barcelona)

MSC:

03B52	Fuzzy logic; logic of vagueness
03G25	Other algebras related to logic

Keywords:

fuzzy logic; propositional logic; finite axiomatization