Contextual decision making with degrees of belief

This paper gives a brief overview of the classical contextual pattern recognition problem. It is shown that the difficulty of this problem is really associated with the determination and use of the support of the joint prior distribution of the category labels. It is indicated how the consistent labeling framework can be used to define the support of the joint prior. It is then shown that this formulation of the problem can be generalized, and a general propositional logic framework which not only defines the support of the joint prior but also permits a calculation to be made evaluating the joint prior for any given set of joint labelings is introduced. It is shown that this formulation is indeed a formulation relating to the degree of belief. A formal system for the degree of belief in terms of an operational probability meaning is developed. The degree of belief in a proposition is exactly the probability with which the proposition can be asserted. It is then shown how the classical contextual problem can be generalized in the belief framework