Is Probability Theory Sufficient for Dealing with Uncertainty in AI: A Negative View

Abstract

An issue which has become a focus of controversy in recent years is whether or not classical probability theory is sufficient for dealing with uncertainty in AI. The topicality of this issue has grown as a result of the emergence of expert systems as one of the principal areas of activity in AI and the development of methods for evidential reasoning based on the Dempster-Shafer theory and fuzzy logic which extend beyond the current boundaries of probability theory. A point of view which is articulated in this paper is that the inadequacy of probability theory stems from its lack of expressiveness as a language of uncertainty, especially for describing fuzzy events and fuzzy probabilities. For example, how would one represent the meaning of the proposition p: it is very likely that Mary is young, in which likely is a fuzzy probability and young is a fuzzy predicate? Furthermore, how can one infer from this proposition an answer to the question: What is the likelihood that Mary is not very young? We show through examples that problems of this type – problems which do not lend themselves to solution by conventional probability-based methods – can be dealt with effectively through the use of fuzzy logic.