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

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 de ned 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.