Axiomatizations of standard algebras for fuzzy PC by use of truth constants (Q2714753)
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scientific article; zbMATH DE number 1607264
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Axiomatizations of standard algebras for fuzzy PC by use of truth constants |
scientific article; zbMATH DE number 1607264 |
Statements
2 July 2001
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triangular norm
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fuzzy logic
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fuzzy propositional calculus
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propositional language
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basic logic
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Axiomatizations of standard algebras for fuzzy PC by use of truth constants (English)
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The paper summarizes basic facts on the approach to fuzzy logic described in detail by Hájek [\textit{P. Hájek}, Metamathematics of fuzzy logic, Kluwer, Dordrecht (1998; Zbl 0937.03030)]. Then it investigates the logic based on a t-norm which is an ordinal sum of the Łukasiewicz t-norm and the product t-norm. The nontrivial idempotent of this t-norm induces a necessity to introduce an additional truth constant. An axiomatization and completeness theorem for this logic are presented.
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