  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.
