From imprecise to granular probabilities

Gert de Cooman’s work is an important contribution to a better understanding of how to deal with imprecise probabilities. But there is an important issue which is not addressed. How can imprecise probabilites be dealt with not in isolation but in the broader context of imprecise probability distributions, imprecise events and imprecise relations? What is needed for this purpose is the concept of granular probability—a probability which is defined in terms of a generalized constraint of the form X isr R, where X is the constrained variable, R is a constraining realtion of r is an indexing variable which defines the modality of the constraint, that is, its semantics. A few examples are used as illustrations. © 2005 Elsevier B.V. All rights reserved.