Stratified inductive hypothesis generation

Abstract

In this paper first we study the enumeration technique, as essentially the only method of the inductive inference, comparing it with best strategies. We conclude that the original enumeration strategy doesn't usually from experience: it is controlled by mistakes or of negative feedback. We define a special subclass of enumeration strategies that is called asymptotic ones. It seems that such strategies are closer to the concept of learning than the original ones. Their hypotheses are divided into subhypotheses and, because of using these, they are quicker in computing and, because of their positive feedback technique, they are more stable in working than the original ones. We define also a new inductive inference type (more exactly infinite families of identification and one of them is just the BC identification) that is called asymptotic inference showing the connection with asymptotic strategies. In this type identification is made gradually by better and better hypotheses. In this way the growth of the hypothetic knowledge, i.e. the learning, can be described in the process of identification. It seems to be useful in the practice. In this meaning even also certain non-recursive functions are approximable. We belive that the criteria of asymptotic inference are more natural requirements for intuition than the earlier ones.