Concept Graphs as Semantic Structures for Contextual Judgment Logic

This paper presents a mathematization of the philosophical doctrine of judgments as an extension of the mathematization of the philosophical doctrine of concepts developed in Formal Concept Analysis. The chosen approach was strongly stimulated by J. F. Sowa’s theory of conceptual graphs. The mathematized conceptual graphs, called concept graphs, are mathematical semantic structures based on formal contexts and their formal concepts; those semantic structures are viewed as formal judgments in the underlying Contextual Judgment Logic. In this paper concept graphs are systematically built up starting with simple concept graphs in section 2 and continuing with existential concept graphs in section 3, with implicational and clausal concept graphs in section 4, and finally with generalizations of concept graphs in section 5. Examples are illustrating the different types of concept graphs.