Layman's probability theory: A calculus for reasoning with linguistic likelihood

Abstract

This paper distinguishes between the task of modeling chance occurrences in the physical world and that of modeling natural human reasoning about such occurrences. It is proposed that everyday common sense often prescribes that the probabilistic and, which corresponds to the joint probability of physical events, should be expressed in terms of the arithmetic min operation, and that it is dual, the or, should be couched in terms of the arithmetic max. Thus, in effect, it is proposed that the logic normally associated with the theory of fuzzy sets can be adapted as a kind of “layman's probability theory”. The rationale for such an “erroneous” model of probability is that such seems to underly natural human decision making in the face of uncertainty. In the interests of modeling and, to whatever extent possible, replicating such decision processes, it is of interest to properly encode the underlying logics. The crux of the article it to present such an encoding as a new kind of formal logical system for reasoning with linguistic likelihood, i.e., with fuzzy terms such as likely, very likely, somewhat unlikely, etc. It is verified that the system allows for semantically coherent expression of the desired probablistic arguments.