A basic mathematical framework for conceptual graphs

Based on the original idea of Sowa on conceptual graph and a recent formalism by Corbett on ontology, this paper presents a rigorous mathematization of basic concepts encountered in the conceptual structure theory, including canon, ontology, conceptual graph, projection, and canonical formation operations, with the aim of deriving their mathematical properties and applying them to future research and development on knowledge representation. Our proposed formalism enhances the conceptual structure theory and enables it to compare favorably with other alternative methods such as the formal concept analysis theory.