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The form and justification of inductive inference rules depend strongly onthe representation of uncertainty. This paper examines one genericrepresentation, namely, incomplete information. The notion can be formalized bypresuming that the relevant probabilities in a decision problem are known onlyto the extent that they belong to a class K of probability distributions. Theconcept is a generalization of a frequent suggestion that uncertainty berepresented by intervals or ranges on probabilities. To make the representationuseful for decision making, an inductive rule can be formulated whichdetermines, in a well-defined manner, a best approximation to the unknownprobability, given the set K. In addition, the knowledge set notion entails anatural procedure for updating -- modifying the set K given new evidence.Several non-intuitive consequences of updating emphasize the differencesbetween inference with complete and inference with incomplete information.

Inductive Inference and the Representation of Uncertainty