Revising Incompletely Specified Convex Probabilistic Belief Bases
  We propose a method for an agent to revise its incomplete probabilistic
beliefs when a new piece of propositional information is observed. In this
work, an agent's beliefs are represented by a set of probabilistic formulae --
a belief base. The method involves determining a representative set of
'boundary' probability distributions consistent with the current belief base,
revising each of these probability distributions and then translating the
revised information into a new belief base. We use a version of Lewis Imaging
as the revision operation. The correctness of the approach is proved. The
expressivity of the belief bases under consideration are rather restricted, but
has some applications. We also discuss methods of belief base revision
employing the notion of optimum entropy, and point out some of the benefits and
difficulties in those methods. Both the boundary distribution method and the
optimum entropy method are reasonable, yet yield different results.
