From Ordered Beliefs to Numbers: How to Elicit Numbers Without Asking for Them (Doable but Computationally Difficult)

One of the most important parts of designing an expert system is elicitation of the expert's knowledge. This knowledge usually consists of facts and rules. Eliciting these rules and facts is relatively easy, the more complicated task is assigning weights (numerical or interval-valued degrees of belief) to different statements from the knowledge base. Expert 1 often cannot quantify their degrees of belief, but they can order them (by suggesting which statements are more reliable). It is, therefore, reasonable to try to reconstruct the degrees of belief from such an ordering. In this paper, we analyze when such a reconstruction is possible, whether it lead to unique values of degrees of belief, and how computationally complicated the corresponding reconstruction problem can be. 1 How to Elicit Numerical Degrees of Belief Without Asking for Them: Formulation of the Problem It is necessary to describe degrees of belief. The core of a knowledgebased system is a body of knowle..