Toward a perception-based theory of probabilistic reasoning with imprecise probabilities

Abstract

The perception-based theory of probabilistic reasoning which is outlined in this paper is not in the traditional spirit. Its principal aim is to lay the groundwork for a radical enlargement of the role of natural languages in probability theory and its applications, especially in the realm of decision analysis. To this end, probability theory is generalized by adding to the theory the capability to operate on perception-based information, e.g., “Usually Robert returns from work at about 6 p.m.” or “It is very unlikely that there will be a significant increase in the price of oil in the near future”. A key idea on which perception-based theory is based is that the meaning of a proposition, p, which describes a perception, may be expressed as a generalized constraint of the form X is r R, where X is the constrained variable, R is the constraining relation and is r is a copula in which r is a discrete variable whose value defines the way in which R constrains X. In the theory, generalized constraints serve to define imprecise probabilities, utilities and other constructs, and generalized constraint propagation is employed as a mechanism for reasoning with imprecise probabilities as well as for computation with perception-based information.