On the optimal inductive inference scheme from the view point of source coding

Summary form only given, as follows. Inference of predicate logic, which is widely used for representation of knowledge in artificial intelligence (AI) systems, is discussed from the viewpoints of source coding and decision theory. Since inference in logic can be regarded as some kind of information transformation, an analogy between inference and source coding can be observed. Inductive inference is regarded as source encoding, because observed facts or examples are compressed into an axiom similar to the compression of a source sequence into a code word. On the other hand, deductive inference is interpreted as decoding. From the viewpoint of decision theory, inductive inference is regarded as the decision problem selecting the collect axiom which represents an observing world. A new inductive inference scheme which induces the minimum Bayes risk is proposed. A method for selecting the axiom which represents the finite observed facts by the minimum description length code is shown.