On Standard Completeness for Non-commutative Many-Valued Logics

In this paper we present two methods for proving the standard completeness for psMTLr logic: the original one given by Jenei and Montagna [1] and an alternative proof based on Horcik’s method for proving standard completeness theorems. Further, we introduce two extensions of psMTLr logic that still enjoy the standard completeness, i.e. psSMTLr and psIMTLr logics.