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An important issue in diagnostic problem solving is how to generate and rank plausible hypotheses for a given set of manifestations. Since the space of possible hypotheses can be astronomically large if multiple disorders can be present simultaneously, some means is required to focus an expert system's attention on those hypotheses most likely to be valid. A domain-independent algorithm is presented that uses symbolic causal knowledge and numeric probabilistic knowledge to generate and evaluate plausible hypotheses during diagnostic problem solving. Given a set of manifestations known to be present, the algorithm uses a merit function for partially completed competing hypotheses to guide itself to the provably most probable hypothesis or hypotheses.