A DESCRIPTION OF A SET OF HYPOTHESES FOR SYSTEM IDENTIFICATION PROBLEM*

Abstract

Abstract This paper concerns the system identification process which is a specific form of the hypothetico-deductive process. More specifically, this paper deals with the inductive inference, i.e., with the process of generating a set of hypotheses σ(E) that explain a given finite set of input-output experiments performed on a finite sequential system being identified. It is shown that Seσ(E) if and only if there exists a homomorphism of a basic hypothesis explaining E, into S. Next, a set of hypotheses σ1(E). defined as follows: Seσ1(E) if E is structure-complete w.r.t. S, is considered. Then it is proved that Seσ1(E) if and only if there exists a full homomorphism of a basic hypothesis onto S. Some important methodological consequences of obtained results are derived. Finally, relationship linking the properties of a system identification algorithm is investigated.