Within probability theory, one must be concerned with what one thinks before new conditions are presented (i.e. the "priors" or prior probabilities). Richard Jeffrey presented a generalization of ordinary conditionalization to update a "prior" in the light of new evidence that dictates a reassessment of the probabilities of members of some partition of a sample space. Dr. Wagner is studying a generalization of Jeffrey's conditionalization in which new evidence bounds the possible revisions of a prior below by a type of lower probability first studied by Dempster, and later abstractly characterized and termed a belief function by Shafer. As an anticipated philosophical consequence of this study, Dr. Wagner hopes to show the superiority of Jeffrey-type approaches to updating over mechanical updating methods such as maxent (and to establish that it is simple a fluke that the results of Jeffrey's rule coincide with those of maxent,since this is not the case for the natural generalization of Jeffrey's rule which he proposes). An additional aim is to establish a clear distinction between conditionalization and symmetric combination techniques such as Dempster's rule. Finally, he hopes to show that Dempster's construction of lower probabilities provides a fully satisfactory response to Carnap's demand for a reasoned construction of the new probabilities on a Jeffrey partition.
