Hierarchy of Knowledge Levels Implemented in a Rule-Based Production System to Calculate Bounds on the Size of Intersections and Unions of Simple Sets

摘要

In this paper, the work is combined in the implementation of a rule based system to produce upper and lower bounds and estimates as to the size of intersections and unions of simple sets. The system constructed for this paper uses the hierarchy of knowledge levels as the tabulated statistics in the database abstract. The system is tested and analyzed to determine the advantages and disadvantages of increasing the knowledge level of the database abstract used for the calculation and of varying the number of partitions used in constructing the database abstracts. The paper also discusses the implementation details encountered during the construction of this system in the PROLOG programming language.