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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

Citations:

Zbl 0966.03022
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Full Text: DOI

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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