Roles of Diagrammatic Information for the Discovery of Geometrical Theorems

Knowledge discovery is one of the humans' most creative activities. As is often pointed out, humans often draw figures in the process of reasoning and problem solving. Diagrammatic information from a figure gives us numerical and relational data for reasoning, and it also gives us cues for controlling reasoning. The author has developed four discovery systems in the domain of plane geometry. These systems automatically draw several forms of figures and observe the figures in order to acquire geometrical data. The data are used for extracting numerical expressions needed for discovering theorems, controlling discovery processes in order to avoid combinatorial explosion, and evaluating the usefulness of generated numerical expressions. As an approach of automated scientific discovery, this paper discusses the roles of diagrammatic information in the process of knowledge discovery.