Theory of Sequential Events

Abstract

The article deals with the problem of inductive learning and predicting in dynamic processes, which can be formally represented as time series of atomic events. The central notion of sequential event is characterised as a finite subsequence of adjacent atomic events in a series. In the first part of the article an algorythmic model of learning is introduced. The criterion of learning is based on the frequency of a particular sequential event and on the time-distance of its previous occurrences from the moment of learning. The second part deals with the problem of evaluation of hypotheses in the process of predicting sequential events. A first order language of sequential events and axiomatic theory of sequential events are defined. The theory is proved to be consistent (a model of the theory is constructed). Then a probabilistic evaluation function for sequential events is defined as an analogy of Carnapian confirmation function. In the conclusion this probabilistic evaluation is discussed from the point of view of the foundations of probability.