Most approaches to model-based diagnosis describe a diagnosis for a system as a set of failing components that explains the symptoms. In order to characterize the typically very large number of diagnoses, usually only the minimal such sets of failing components are represented. This method of characterizing all diagnoses is inadequate in general, in part because not every superset of the faulty components of a diagnosis necessarily provides a diagnosis. In this paper we analyze the notion of diagnosis in depth exploiting the notions of implicate/implicant and prime implicate/implicant. We use these notions to propose two alternative approaches for addressing the inadequacy of the concept of minimal diagnosis. First, we propose a new concept, that of kernel diagnosis, which is free of the problems of minimal diagnosis. Second, we propose to restrict the axioms used to describe the system to ensure that the concept of minimal diagnosis is adequate.
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