Contexts and concepts, abstraction duals

  • John Esch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 835)


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.


Conceptual Graphs Concepts Contexts Black Box White Box Individuals Aggregations Expansion Contraction Relation Instances 


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  1. [1]
    John F. Sowa, Conceptual Structures: Information Processing in Mind and Machine, Addison Wesley, 1984.Google Scholar
  2. [2]
    John F. Sowa, Conceptual Graphs Summary, Conceptual Structures: Current Research and Practice, Ellis Horwood, 1992.Google Scholar
  3. [3]
    Esch, John, Contexts as White Box Concepts, Proceedings First International Conference on Conceptual Structures, Quebec City, Canada, 1993.Google Scholar
  4. [4]
    Esch, Nagle, Yim & Gerhob, Resolving Polymorphism in the Theory of Conceptual Graphs, Fourth Annual Workshop on Conceptual Graphs, August 1989.Google Scholar
  5. [5]
    John W. Esch Graphical Displays and Polymorphism, Conceptual Structures: Current Research and Practice, Ellis Horwood, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • John Esch
    • 1
  1. 1.Unisys Government Systems GroupSt. Paul

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