Contexts and concepts, abstraction duals

Abstract

In the theory of conceptual graphs [1], it is not clear how a concept, with a referent that is a graph, differs from a context containing the same graph. In a previous paper, ”Contexts as White Box Concepts” [3], the author began exploring the relationship of contexts and concepts in the theory of conceptual graphs. It pointed out a strong relationship between contexts with type labels and type definitions with differentia and formalized that relationship in a couple of theorems. This paper reviews and generalizes those results. First, the same analysis is applied to individuals to show that aggregations can be thought of as white box individuals. Second, the strong parallel between the prior and new application is generalized. This generalization leads to the definition of a new operator and its inverse, referent expansion and contraction. It also results in the observation that a concept with a graph or graphs in its referent field is just another notation for a context. Lastly, another approach to relation instances is presented and used to map an arbitrary context to a corresponding concept. That step establishes the hypothesis that concepts and contexts are abstraction duals.