Together with Professor Shigeo Nagai, my teacher, I engage myself in studying the extension and generalization of the theory of inductive probability and the theory of semantic information. To state only a result of my part in our reseaches, therefore, is the aim of this monograph.
The mathematical field of the theory of semantic information belongs to the theory of inductive probability, and the philosophical field of it to semantics. So, by extending and generalizing the theory of inductive probability, most of the extension and generalization of the theory of semantic information can be done syntactically; and the extended language system can be the semantical one.
In the last I extended the theory of inductive probability. Here I will state, therefore, the theory of inductive probability, or the theory of semantic information, based on the S^KN language system, as compared with that based on the LS^πS^NN language system of R. Carnap and Bar-Hillel.