Playing with Diagrams

Abstract

This paper extends work that developed a programmed model of reasoning about geometric propositions. The system reasons by manipulating representations of diagrams and noticing newly emerged facts that are construed as inferences. The system has been explored as a means of verifying diagrammatic demonstrations of classical geometric propositions and for constructing diagrammatic demonstrations of conclusions supplied for the system. The process of discovering propositions to be demonstrated is a more difficult task. This paper argues that central to the discovery process is systematic manipulation of diagrams – playing – and observing consistent relations among features of the diagram as manipulations are made and observed. The play results in the creation of an "episode" of diagram behaviors which is examined for regularities from which a general proposition might be proposed. The paper illustrates this process and discusses the advantages and limitations of this system and of other computational models of diagrammatic reasoning.