Expert systems commonly employ some means of drawing inferences from domain and problem knowledge, where both the knowledge and its implications are less than certain. Methods used include subjective Bayesian reasoning, measures of belief and disbelief, and the Dempster-Shafer theory of evidence. Analysis of systems based on these methods reveals important deficiencies in areas such as the reliability of deductions and the ability to detect inconsistencies in the knowledge from which deductions are made. A new system called INFERNO addresses some of these points. Its approach is probabilistic but makes no assumptions whatsoever about the joint probability distributions of pieces of knowledge, so the correctness of inferences can be guaranteed. INFERNO informs the user of inconsistencies that may be present in the information presented to it, and can make suggestions about changing the information to make it consistent. An example from a Bayesian system is reworked, and the conclusions reached by that system and INFERNO are compared.