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Most model-based approaches to fault diagnosis of discrete-event systems (DESs) require a complete and accurate model of the system to be diagnosed. However, the discrete-event model may have arisen from abstraction and simplification of a continuous time system or through model building from input-output data. As such, it may not capture the dynamic behavior of the system completely. In this paper, we address the problem of diagnosing faults, given an incomplete model of the discrete-event system. When the model is incomplete, discrepancies will arise between the actual output and the output predicted by the model. We introduce learning into the diagnoser construction by forming hypotheses that explain these discrepancies. We view the process of generating and evaluating hypotheses about the model of the system as an instance of the set-cover problem, which we formalize using parsimonious covering theory. We describe in detail the construction of the learning diagnoser, which not only performs fault diagnosis but also attempts to learn the missing model information. If the model is complete, the learning diagnoser reduces to the standard state-based diagnoser. Examples are provided to illustrate how learning and diagnosis can be simultaneously achieved through the learning diagnoser.