The Probability of a Possibility: Adding Uncertainty to Default Rules
  We present a semantics for adding uncertainty to conditional logics for
default reasoning and belief revision. We are able to treat conditional
sentences as statements of conditional probability, and express rules for
revision such as "If A were believed, then B would be believed to degree p."
This method of revision extends conditionalization by allowing meaningful
revision by sentences whose probability is zero. This is achieved through the
use of counterfactual probabilities. Thus, our system accounts for the best
properties of qualitative methods of update (in particular, the AGM theory of
revision) and probabilistic methods. We also show how our system can be viewed
as a unification of probability theory and possibility theory, highlighting
their orthogonality and providing a means for expressing the probability of a
possibility. We also demonstrate the connection to Lewis's method of imaging.
