  We start by defining an approach to non-monotonic probabilistic reasoning in
terms of non-monotonic categorical (true-false) reasoning. We identify a type
of non-monotonic probabilistic reasoning, akin to default inheritance, that is
commonly found in practice, especially in "evidential" and "Bayesian"
reasoning. We formulate this in terms of the Maximization of Conditional
Independence (MCI), and identify a variety of applications for this sort of
default. We propose a formalization using Pointwise Circumscription. We compare
MCI to Maximum Entropy, another kind of non-monotonic principle, and conclude
by raising a number of open questions
