Neat Explanation of Proof Trees

It is essential that the reasoning of an expert system can be ex-­ plained and justified. In the paper simple ideas for providing com-­ prehensive explanations of deductions are presented. The method is to transform the proof tree to a more comprehensive proof tree from which a neat explanation directly can be extracted. The transformation of proof trees is a way to view the problem of explaining the reasoning of an expert system. The ideas presented in this paper are easy to implement. Furthermore, the transformation for reducing chains of specifications of a concept seems to be applica-­ ble in general. The transformation for introducing a new name for a compilation of concepts depends on the problem domain. I I N T R O D U C T I O N A fundamental part of an expert system design is its ability to ex-­ plain and justify a line of reasoning (Parsaye, 1983), (Swartout, 1981), (Walker, 1983), (Wallis and Shortliffe, 1984). In this paper we outline some principles for providing comprehensible explanations of deduc-­ tions, i.e. why a fact is derived. The interesting problem of explaining why a fact cannot be derived is not the subject of this paper. We will focus on expert systems designed and implemented in a logic programming environment. The domain knowledge is expressed as an axiom set in the form of Horn-­clauses. A program clause either describes a sentence that is unconditionally true, such as "The color of grass is green" Color(Grass,Green) <-­ or a conditional sentence, "x and y are playmates if both x and y are children and live at the same place" In a logic programming language such as Prolog (Pereira et a/, 1977), (Carlsson and Kahn, 1984) answers to questions are deduced from the set of axioms by resolution (Robinson, 1979). I I P R O O F T R E E S We illustrate the ideas with easy and comprehensible relations. Two persons x and y are related if they have an ancestor in com-­ mon. Anyone who is either a father or a mother is a parent. In order to draw conclusions about family-­relations concerning spe-­ cific individuals we need some basic facts about the fathers and moth-­ ers. We state that: the father of Ada is John, . . . , the mother of T im is Pia. Let us study an AND-­tree constructed for the proof of the formula Rdated(Ada,Tom). The root of the proof tree is Related(Ada,Tom). When both Ancestor(Ada,z) and Ancestor(Tom,z) are deduced we can apply rule (1) to obtain Related(Ada,Tom). In Figure 1 below, the complete proof tree is shown.