A Mathematical Model of Deductive and Non-Deductive Inferences

抄録

Induction and abduction are well known non-deductive inferences. We shall propose a view that design is also another form of non-deductive inference, and give a mathematical model of deductive and non-deductive inferences based on Barwise and Seligman's mathematical theory of information flow. In our model, inferences are classified into three categories, and we can show that deduction and abduction are in the same category, although induction is different. Furthermore, we shall show also that non-deductive inferences are interpretable mutually, and investigate also mathematical properties of the model. In particular, we shall prove a generalized version of the Abstract Completeness Theorem by Barwise and Seligman.