Jeffrey-like rules of conditioning for the Dempster-Shafer theory of evidence

AbstractJeffrey's rule of conditioning is a rule for changing an additive probability distribution when the human perception of new evidence is obtained. It is a generalization of the normative Bayesian inference. Shafer showed how Jeffrey's generalization of Bayes' rule of conditioning can be reinterpreted in terms of the theory of belief functions. But Shafer's approach is different from the normative Bayesian approach and is not a straight generalization of Jeffrey's rule. There are situations in which we need inference rules that may well provide a convenient generalization of Jeffrey's rule. Therefore we propose new rules of conditioning motivated by the work of Dubois and Prade. Although the weak and strong conditioning rules of Dubois and Prade are generalizations of Bayesian conditioning, they fail to yield Jeffrey's rule as a special case. Jeffrey's rule is a direct consequence of a special case of our conditioning rules. Three kinds of normalizations in the rules of conditioning are discussed