Fuzzy Logics with Noncommutative Conjuctions

Pseudo-BL-algebras were introduced by di Nola, Georgescu and Iorgulescu as a non-commutative generalization of BL-algebras. BL-algebras serve as general semantics of the basic fuzzy logic BL. Here we develop a corresponding generalization psBL (pseudo-basic fuzzy logic) of the logic BL and show the relation of psBL to pseudo-BL-algebras.