Knowing About Diagrams

Abstract

Understanding diagrams and using themin problem solving requires extensive knowledge about the properties of diagrams, what diagram elementsd enote, how their parts are distinguished and referenced, how they relate to linguistic statements, and so forth. This knowledge is mostnaturally represented linguistically. Nonetheless, diagrams or imaginalre presentations of themare usedin substantive non-linguistic waysas part of the problem solving process. The interaction of linguistic and diagrammatic representations must be understoodin order to construct a theory of diagrammatic reasoning. In this paper, an example is examined to illustrate some of the waysin whichdiagram manipulation may be used in geometric reasoning and to informally identify some of the knowledge necessary for suchreasoning.