Bayesian and Non-Bayesian Evidential Updating

Four main results are arrived at in this paper. 1 Closed convex sets of classical probability functions provide a representation of belief that includes the representations provided by Shafer probability mass functions as a special case. 2 The impact of uncertain evidence can be formally represented by Dempster conditioning, in Shafers framework. 3 The impact of uncertain- evidence can be formally represented in the framework of convex sets of classical probabilities by classical conditionalization. 4 The probability intervals that result from DempsterShafer updating on uncertain evidence are included in and may be properly included in the intervals that result form Bayesian updating on uncertain evidence.