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.