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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.

##### MSC:
 03B52 Fuzzy logic; logic of vagueness 03G25 Other algebras related to logic
##### Keywords:
fuzzy logic; propositional logic; finite axiomatization
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