Medical science often suffers from having so few data and so much imperfect knowledge that a rigorous probabilistic analysis, the ideal standard by which to judge the rationality of a physician's decision, is seldom possible. Physicians nevertheless seem to have developed an ill-defined mechanism for reaching decisions despite a lack of formal knowledge regarding the interrelationships of all the variables that they are considering. This report proposes a quantification scheme which attempts to model the inexact reasoning processes of medical experts. The numerical conventions provide what is essentially an approximation to conditional probability, but offer advantages over Bayesian analysis when they are utilized in a rule-based computer diagnostic system. One such system, a clinical consultation program named mycin, is described in the context of the proposed model of inexact reasoning.