This article consists of two parts. Part I considers the so-called problem of induction, viz., the history of its genesis and elaboration, and formulates the main principles and logical tools of the JSM method for automatic hypothesis generation, including JSM reasoning. JSM reasoning is demonstrated to be a synthesis of three cognitive procedures: induction, analogy, and abduction. Two possible kinds of abduction are considered. Part I focuses on formal tools to be used for the solution of the natural-scientific problem of induction. Part II formulates the procedural semantics for predicates that are used to formalize JSM reasoning, considers quasi-axiomatic (open) theories used to represent knowledge in intelligent systems, determines the means for assessing the quality of JSM-reasoning results, and, finally, suggests a solution of the naturalscientific problem of induction for intelligent systems. Part I was published in the journal Nauchno-Tekhnicheskaya Informatsiya, ser. 2, 2013, no. 9, pp. 1---29. Part II was published in the journal Nauchno-Tekhnicheskaya Informatsiya, ser. 2, 2013, no. 12, pp. 1---26.