## The Ł$$\Pi$$ and Ł$$\Pi\frac{1}{2}$$ propositional and predicate logics.(English)Zbl 0994.03015

Summary: This paper has two main goals. The first goal is to show a different axiomatic system for the Ł$$\Pi$$ and Ł$$\Pi{1\over 2}$$ propositional logics. These propositional logics were introduced by F. Esteva, L. Godo and F. Montagna [Arch. Math. Logic 40, 39-67 (2001; Zbl 0966.03022)] and they are combinations of the Łukasiewicz and the product logic (together with the constant $${1\over 2}$$ in case of the Ł$$\Pi{1\over 2}$$ logic). The second goal is to show an axiomatic system and the completeness theorem for a predicate version of the Ł$$\Pi$$ and Ł$$\Pi{1\over 2}$$ propositional logics. It will be shown that Gödel, product and Łukasiewicz predicate logics are contained in the Ł$$\Pi\forall$$ logic.

### MSC:

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

Zbl 0966.03022
Full Text:

### References:

 [1] L. Esteva, F. Godo, F. Montagna, The Ł $$Π$$ and Ł $$Π12$$ logics: two complete fuzzy systems joining Łukasiewicz and product logics. Arch. Math. Logic, to appear. · Zbl 0966.03022 [2] Hájek, P., Metamathematics of fuzzy logic, (1998), Kluwer Dordrecht · Zbl 0937.03030
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