Knowing About Diagrams

Understanding diagrams and using them in problem solving requires extensive knowledge about the properties of diagrams, what diagram elements denote, how their parts are distinguished and referenced, how they relate to linguistic statements, and so forth. This knowledge is most naturally represented linguistically. Nonetheless, diagrams or imaginal representations of them are used in substantive non-linguistic ways as part of the problem solving process. The interaction of linguistic and diagrammatic representations must be understood in order to construct a theory of diagrammatic reasoning. In this paper, an example is examined to illustrate some of the ways in which diagram manipulation may be used in geometric reasoning and to informally identify some of the knowledge necessary for such reasoning.