In this paper, medical diagnosis is viewed as a two-stage process: medical knowledge is first interpreted in a diagnostic sense; next, observed findings are interpreted with respect to this interpreted knowledge and a given hypothesis, yielding a diagnosis. A new set-theoretical framework is introduced that captures this view of diagnosis; it is used to formalize various notions of diagnosis, those proposed in the literature included. Next, a new theory of flexible diagnosis, called refinement diagnosis, is proposed and defined in terms of this framework. Relationships with notions of diagnosis known from the literature are investigated.