計算機による図形的制約に基づく発見手法

抄録

This paper describes a new method of discovering theorems in a plane geometry domain. In order to discover useful theorems from a figure, the following subjects should be discussed : the contents of acquired data by observing the figure, the techniques for avoiding combinatorial explosion of expressions, and the criteria for choosing useful theorems from generated expressions. Our discovery method is based on the sides in a given figure. All the geometric relations among sides are observed from a figure. Deduced expression which shows the relation of closely located sides in the figure are regarded as a useful theorem. It is because a human often considers such an expression to be an important theorem. Observed geometric relations among sides are used for both choosing useful theorems and avoiding combinatorial explosion of generated expressions. Although most of the methods of previous discovery systems such as AM, KEKADA and IDS require much initial knowledge for evaluating the usefulness of generated knowledge, our method needs little initial knowledge about plane geometry. Our discovery method has been implemented in a system called PLANET, a discovery system for plane geometry theorems. PLANET has succeeded in discovering many useful geometry theorems and trigonometric formulas, including Menelaus' theorem, Ceva's theorem, and addition theorems of trigonometric functions, through trial and error.