Distances between Predicates in By-Analogy Reasoning Systems

Abstract

The purpose is to develop expert systems where by-analogy reasoning is used. Knowledge “closeness” problems are known to frequently emerge in such systems if knowledge is represented by different production rules. To determine a degree of closeness for production rules a distance between predicates is introduced. Different types of distances between two predicate value distribution functions are considered when predicates are “true”. Asymptotic features and interrelations of distances are studied. Predicate value distribution functions are found by empirical distribution functions, and a procedure is proposed for this purpose. An adequacy of obtained distribution functions is tested on the basis of the statistical 2 χ –criterion and a testing mechanism is discussed. A theorem, by which a simple procedure of measurement of Euclidean distances between distribution function parameters is substituted for a predicate closeness determination one, is proved for parametric distribution function families. The proposed distance measurement apparatus may be applied in expert systems when reasoning is created by analogy.