Inductive Inference and the Representation of Uncertainty
  The form and justification of inductive inference rules depend strongly on
the representation of uncertainty. This paper examines one generic
representation, namely, incomplete information. The notion can be formalized by
presuming that the relevant probabilities in a decision problem are known only
to the extent that they belong to a class K of probability distributions. The
concept is a generalization of a frequent suggestion that uncertainty be
represented by intervals or ranges on probabilities. To make the representation
useful for decision making, an inductive rule can be formulated which
determines, in a well-defined manner, a best approximation to the unknown
probability, given the set K. In addition, the knowledge set notion entails a
natural procedure for updating -- modifying the set K given new evidence.
Several non-intuitive consequences of updating emphasize the differences
between inference with complete and inference with incomplete information.
