Summary: Most expert knowledge is ill-defined and heuristic. Therefore, many present-day rule-based expert systems include a mechanism for modeling and manipulating imprecise knowledge. For a long time, probability theory has been the primary quantitative approach for handling uncertainty. Other (mathematical) models of uncertainty have been proposed during the last decade, several of which depart from probability theory. In this paper, so-called inference networks are introduced to demonstrate the application of such a model for inexact reasoning in a rule-based top- down reasoning expert system. This approach enables the formulation of a conceptual model for inexact reasoning in rule-based systems. This conceptual model is used to show some inadequacies in the certainty factor model, a model that has been proposed by the authors of MYCIN system and that has actually been applied in expert systems. A syntactically correct reformulation of the certainty factor model is proposed, and this new formalism is used to discuss some of the model’s properties.