Relation Graphs: A Structure for Representing Relations in Contextual Logic of Relations

Abstract

Contextual Logic of Relations (CLR) is based on Formal Concept Analysis (FCA) and Peircean Algebraic Logic (PAL). The aim of the paper is to introduce relation graphs as an algebraic structure for representing relations and operations on relations in Contextual Logic of Relations. It is shown that each relation graph of a relation context family uniquely represents an extent of a relation described by a first order logic formula. In reverse, each compound relation of a relation context family can be represented by a relation graph. A graphical representation of relation graphs highly corresponds to a graphical system of PAL. The formal definition of relation graphs is intended to clarify correspondences between PAL and (existential semi-) concept graphs as well as existential graphs.