MP and MT-implications on a Finite Scale

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 satisfying these properties for a given smooth t-norm T1. The non-smooth case is also discussed for a special family of t-norms.

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