Modus ponens and modus tollens in discrete implications

Abstract

This paper is devoted to the study of discrete implications that satisfy modus ponens (MP), modus tollens (MT) or both (MPT). The main goal is to characterize all R, S, QL and D-implications on a finite chain L, derived from smooth t-norms, satisfying these properties for a given smooth t-norm T 1 . The case when T 1 is non-smooth is also discussed for a special family of t-norms.