Preduction: A Common Form of Induction and Analogy

摘要

Deduction, induction, and analogy pervade all our thinking. In contrast with deduction, understanding logical aspects of induction and analogy is still an important and challenging issue of artificial intelligence. This paper describes a logical formalization, called preduction, of common conjectural reasoning of both induction and analogy. By introduction of preduction, analogical reasoning is refined into "preduction + deduction" and (empirical) inductive reasoning is refined into "preduction + mathematical induction". We examine generality of preduction through applications to various examples on induction and analogy.