The existing theory of consistency-based diagnosis and its implementations have proven successful in a number of technical applications. However, they turn out to be inherently limited to a very specific class of systems to be diagnosed: They are tailored for artifacts consisting of components in a fixed structure and they are aimed at a particular kind of diagnosis and repair, namely failing components and their replacement. This thesis presents a generalization of the theory of consistency-based diagnosis, applicable to a much wider class of systems and diagnosis problems, while preserving the approach based on "first principles" and the core of the existing logical foundations. The central contributions are a logical reconstruction of a process-oriented modeling paradigm, a concise characterization of solutions to the diagnostic tasks of situation assessment and therapy recognition, and an algorithmic approach to computing the specified solutions. Finally, an implemented prototype, the Generalized Diagnosis Engine (G+DE) and several extended application examples are presented.