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

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.


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