Generalized Modus Ponens Based on Linguistic Modifiers in a Symbolic Multi-Valued Framework

Abstract

Approximate reasoning is based on a generalization of Modus Ponens, known as Generalized Modus Ponens (GMP). Its principle is that from an observation different but approximately equal to the rule premise, we can deduce a fact approximately equal to the rule conclusion. However, the deduced fact is not obtained with an arbitrary way. A set of axioms are fixed to have coherent and logic results. In this paper, we propose a new rule of GMP in the multi-valued logic framework. Our aim is to provide inference results which checks the axiomatic of approximate reasoning. We propose to use linguistic modifiers in GMP and we explain how it allows having a gradual reasoning.