An Algebraic Structure Theory of Rule Sets. I. A Formalization of Both Production Systems and Decision Tables

摘要

In this paper by a rule we shall mean the form if...then... . A rule set is a collection of rules. We have been using those rules in production systems and decision tables. This paper formalizes both production systems and decision tables as rule sets based on free Boolean algebra and constructs an algebraic structure theory of rule sets. In the formalization we show that we can deal with production systems and decision tables in much the same way, and we define the two-level hierarchical structure (e.g., the free Boolean rule sets and their interpretations) of abstract rule sets (knowledge bases). After formally defining the logical rule system, which is a theoretical model of conventional production systems and decision tables, this paper identifies the concepts of independence and exclusiveness between rules of the system, and derives several fundamental properties between rules and between actions. The theory described in this paper may be useful as a basis for describing, interpreting, analyzing, and synthesizing rule sets (production systems and decision tables) in both the theoretical and practical aspects. (Author)