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A general problem-solving mechanism is described that is especially suited for performing a particular form of abductive inference, or best explanation finding. A problem solver embodying this mechanism synthesizes composite hypotheses by combining simple hypotheses to satisfy explanatory goals. These simple hypotheses are formed by instantiating prestored explanatory "concepts." In this way the problem solver is able to arrive at complex integrated conclusions which are not prestored. A computationally feasible task-specific problem-solving mechanism is presented for a particular information-processing task which is, nevertheless, of very great generality. The task is that of synthesizing coherent composite explanatory hypotheses based upon a prestored and possibly vast collection of hypothesis-generating concepts. This is seemingly a common task of intelligence and potentially a major component of diagnostic reasoning, especially where single-fault assumptions are inappropriate. The mechanism is described both functionally and structurally; that is, the why and what of the main computations are described, together with algorithms that show how each of these computations can be accomplished. The mechanism integrates a classification machine, used for selecting plausible hypotheses, with a specialized means-ends machine, used for assembling a best explanation from the plausible hypotheses thus selected and for pointedly investigating alternative explanations. There are also two other specialized mechanisms for the subsidiary functions of recognizing the applicability of a hypothesis to the situation and of interpreting the situation-specific raw data to satisfy the informational needs of the other components.