点別サーカムスクリプションに基づく孤立式の一般化

抄録

Circumscription is a very useful concept for commonsense and nonmonotonic reasoning. But circumscription is formalized as a higher-order formula, therefore its direct treatment is very difficult. For this problem, Lifschitz proposed equivalent transformations of predicate circumscription into first-order formulas. He showed that a class of predicate circumscription in a solitary formula can be translated into first-order formulas. Also, by using a concept of pointwise circumscription, he showed another class can be translated into first-order formulas. In this paper, we give more powerful transformation rules of predicate circumscription. At first, we discuss and clarify some problems of Lifschitz's transformation methods. Next, we give two transformation rules for simplifying predicate circumscription, which are very important and useful methods to solve the above problems. And we clarify the concept of pointwise circumscription and strengthen Lifschitz's theorem. Finally, we give an equivalent transformation theorem of predicate circumscription into first-order formulas. A class of predicate circumscription which can be translated by the theorem includes Lifschitz's two classes mentioned above as its proper subsets.