Different Forms of Generalized Hypothetical Syllogism with Regard to R-Implications

Abstract

In this paper we investigate the generalized hypothetical syllogism (GHS). We present few versions of the well known GHS equation. We focus our attention on R-implications and give some results concerning left-continuous t-norms. We show some solutions of GHS equations based on the compositional rule of inference and Bandler-Kohout subproduct. Also we sketch the idea of new possible functional equations coming from the GHS.