Resumen de Modus ponens and modus tollens in discrete implications

Margarita Mas Grimalt, Miquel Monserrat Antich, Joan Torrens Sastre

• 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 T1. The case when T1 is non-smooth is also discussed for a special family of t-norms.