Monoidal t-norm based logic

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Authors:
Francesc Esteva
Lluís Godo
Title: Monoidal t-norm based logic : towards a logic for left-continuous t-norms
Journal: Fuzzy Sets and Systems
Volume 124
Number 3
Pages: 271-288
Year: 2001





Abstract

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 isintended 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.