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Monoidal t-norm based logic: Towards a logic for left-continuous t-norms. (English) Zbl 0994.03017

Summary: Hájek’s BL logic is the fuzzy logic capturing the tautologies of continuous t-norms and their residua. In this paper we investigate a weaker logic, MTL, which is intended to cope with the tautologies of left-continuous t-norms and their residua. The corresponding algebraic structures, MTL-algebras, are defined and completeness of MTL with respect to linearly ordered MTL-algebras is proved. Besides, several schematic extensions of MTL are also considered as well as their corresponding predicate calculi.

MSC:

03B52 Fuzzy logic; logic of vagueness
03G25 Other algebras related to logic
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