Monoidal t-norm based logic: towards a logic for left-continuous t-norms

Hajek'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. (C) 2001 Elsevier Science B.V. All rights reserved.