Unification over Constraints in Conceptual Graphs

Abstract

The Conceptual Structures community has recently shown increased interest in methods and formalisms for the use of constraints in Conceptual Graphs (CGs), especially the definition of unification over constraints. None of the recent proposed constraint methods, however, are able to use simple unification methods, and still guarantee that a graph which is structurally valid under the canonical formation rules is also semantically valid in the knowledge domain. Our approach defines a method (and concept type) for constraining real values in the referent of a concept. The significance of our work is that a simple unification operation, using join and type subsumption, is defined which can be used to validate the constraints over an entire unified graph. A useful side-effect is that this constraint method can also be used to define real numbers in a referent.