Modus ponens and modus tollens in discrete implications

Authors:
M. Mas;M. Monserrat;J. Torrens
Affiliations:
Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain;Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain;Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
Venue:
International Journal of Approximate Reasoning
Year:
2008

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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.