On the Revision of Probabilistic Belief States

In this paper we describe two approaches to the revision of probability functions. We assume that a probabilistic state of belief is captured by a counterfactual probability or Popper function, the revision of which determines a new Popper function. We describe methods whereby the original function determines the nature of the revised function. The rst is based on a probabilistic extension of Spohn's OCFs, while the second exploits the structure implicit in the Popper function itself. This stands in contrast with previous approaches that associate a unique Popper function with each absolute (classical) probability function. We also describe iterated revision using these models. Finally, we consider the point of view that Popper functions may be abstract representations of certain types of absolute probability functions, but show that our revision methods cannot be naturally interpreted as conditionalization on these functions.