Cadiag-2-where "Cadiag" stands for "computer-assisted diagnosis"- is an expert system based on fuzzy logic assisting in the differential diagnosis in internal medicine. With its aid, it is possible to derive from possibly vague information about a patient's symptoms, signs, laboratory test results, and clinical findings conjectures about present diseases. In this paper, we provide a mathematical formalization of the inferential mechanism of Cadiag-2. The aim is to have a formal logical calculus at hand which corresponds to the mode of operation of Cadiag-2 and which is among others needed to perform consistency checking of Cadiag-2's medical knowledge base.