  When knowledge is obtained from a database, it is only possible to deduce
confidence intervals for probability values. With confidence intervals
replacing point values, the results in the set covering model include interval
constraints for the probabilities of mutually exclusive and exhaustive
explanations. The Principle of Interval Constraints ranks these explanations by
determining the expected values of the probabilities based on distributions
determined from the interval, constraints. This principle was developed using
the Classical Approach to probability. This paper justifies the Principle of
Interval Constraints with a more rigorous statement of the Classical Approach
and by defending the concept of probabilities of probabilities.
