Concept Graphs as Semantic Structures for Contextual Judgment Logic

In the ICCS 2000 proceedings we introduced negation to simple concept graphs without generic markers by adding cuts to their definition. The aim of this paper is to extend this approach of cuts to simple concept graphs with generic markers. For these graphs, a set-theoretical semantics is presented. After this a modification of Peirce's beta-calculus is provided, and definitions for mappings Φ and Ψ between concept graps and first order logic are given. If we consider both concept graphs and first order logic formulas, together with their particular derivability relations, as quasiorders, Φ and Ψ are mutually inverse quasiorder isomorphisms between them. The meaning of this fact is elaborated. Finally we provide a result that links the semantics of concept graphs and the semantics of first order logic. This result can be used to show that the calculus for concept graphs is sound and complete.