Use of partial functional dependencies to make practical approximate translations among forms of propositional expert systems

Abstract

Decision tables and decision trees have long been used to describe and implement computer programs which classify cases. It also is known that there is a close relationship between them. This however, is mediated by algorithms which tend to be exponential. Decision tables and decision trees can be viewed as propositional system; so can most expert systems. Knowledge-based systems therefore give rise to very large decision tables or trees. Further, it is often convenient to transform an object from one representation to another, so that the exponential algorithms become impracticable. In this paper, we first formalise decision tables, decision trees, cases and rules and the well known relationships among them. We then introduce the concept of equivalence with respect to a set of cases, which enables us to make transformations with algorithms which are linear in the number of cases. Then we introduce the concept of equivalence with respect to a set of constraints (rules), which enables us to perform transformations with algorithms in a sounder, less ad hoc way. The paper evaluates these algorithms by applying them to a large example. These new algorithms permit computationally effective and practically useful transformations for large problems.