Justifying the Principle of Interval Constraints
This work addresses a theoretical issue in probabilistic reasoning for knowledge extraction from databases, but it appears incremental as it focuses on justifying an existing principle with a more rigorous approach.
The paper tackles the problem of ranking mutually exclusive and exhaustive explanations when only confidence intervals for probabilities are available from database knowledge, by justifying the Principle of Interval Constraints that uses expected values based on distributions from these intervals.
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.