Abstract

We investigate induction from the viewpoint of nonmonotonic reasoning. Induction we consider in this paper is descriptive induction. Hypotheses from descriptive induction have the weak property that they only describe rules with respect to the observations and do not realize an inductive leap. In this paper, we define a new form of descriptive induction with circumscription and the idea of explanation and show two procedures for computing it. The new descriptive induction is called circumscriptive induction. By deciding the roles of predicates in circumscription, we can intentionally minimize models of a given inductive problem. By adopting the idea of explanation, we can distinguish between background knowledge and observations. Additionally, we consider the relationship between the way of choosing the roles of predicates in computing circumscription and the property of hypotheses obtained by circumscriptive induction. It is shown that hypotheses from circumscriptive induction reflect a difference between background knowledge and observations and do not realize an inductive leap. We also investigate revision of hypotheses which is as important as generation of hypotheses. In a process of hypothesis revision, a difference between previous induction and circumscriptive induction is clearly characterised.