Probabilistic Interpretations for MYCIN's Certainty Factors

TL;DR

This paper analyzes MYCIN's certainty factors, identifies inconsistencies, and proposes a probabilistic reinterpretation that clarifies assumptions and limitations of the model.

Contribution

It redefines certainty factors in probabilistic terms, revealing their relation to likelihood ratios and discussing implications for inference network assumptions.

Findings

Certainty factors are monotonic transformations of likelihood ratios.

Inconsistencies exist between original certainty factors and combining functions.

Conditional independence and tree structure are necessary for proper uncertainty propagation.

Abstract

This paper examines the quantities used by MYCIN to reason with uncertainty, called certainty factors. It is shown that the original definition of certainty factors is inconsistent with the functions used in MYCIN to combine the quantities. This inconsistency is used to argue for a redefinition of certainty factors in terms of the intuitively appealing desiderata associated with the combining functions. It is shown that this redefinition accommodates an unlimited number of probabilistic interpretations. These interpretations are shown to be monotonic transformations of the likelihood ratio p(EIH)/p(El H). The construction of these interpretations provides insight into the assumptions implicit in the certainty factor model. In particular, it is shown that if uncertainty is to be propagated through an inference network in accordance with the desiderata, evidence must be conditionally independent given the hypothesis and its negation and the inference network must have a tree structure. It is emphasized that assumptions implicit in the model are rarely true in practical applications. Methods for relaxing the assumptions are suggested.