Monoidal t-norm based logic
From Mathfuzzlog
Authors: |
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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.