Advances in the Ł\(\Pi\) and Ł\(\Pi\frac 12\) logics. (English) Zbl 1026.03017

Summary: The Ł\(\Pi\) and Ł\(\Pi\frac 12\) logics were introduced by Godo, Esteva and Montagna. These logics extend many other known propositional and predicate logics, including the three mainly investigated ones (Gödel, product and Łukasiewicz logic).
The aim of this paper is to show some advances in this field. We will see further reduction of the axiomatic systems for both logics. Then we will see many other logics contained in the Ł\(\Pi\) family of logics (namely logics induced by the continuous finitely constructed t-norms and Takeuti and Titani’s fuzzy predicate logic).


03B52 Fuzzy logic; logic of vagueness
03B50 Many-valued logic
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