A Symbolic Generalization of Probability Theory

Abstract

This paper demonstrates that it is possible to relax the commitment to numeric degrees of belief while retaining the desirable features of the Bayesian approach for representing and changing states of belief. We first present an abstract representation of states of belief and an associated notion of conditionalization that subsume their Bayesian counterparts. Next, we provide some symbolic and numeric instances of states of belief and their conditionalizations. Finally, we show that patterns of belief change that make Bayesianism so appealing do hold in our framework. Introduction Representing states of belief and modeling their dynamics is an important area of research in AI that has many interesting applications. A number of formalisms for this purpose have been suggested in the literature [ Aleliunas, 1988; Bonissone, 1987; Dubois and Prade, 1988; Ginsberg, 1988; Pearl, 1988; Shenoy, 1989; Spohn, 1990 ] but Bayesian formalisms [ Pearl, 1988 ] seem to be among the best we know. Here...