CADIAG-1 and CADIAG-2 (Computer-Assisted DIAGnosis) are medical expert systems especially designed for ill-defined areas such as internal medicine. Both systems are being tested in the setting of a medical information system. With respect to their knowledge representation, CADIAG-1 has obvious advantages in totally ill-defined areas such as syndromes in internal medicine, whereas CADIAG-2 seems more suited for domains with basic laboratory programs, e.g., hepatology or gall bladder and bile duct diseases. The formalization of relationships between medical entities led to first-order predicate calculus formulas in the case of CADIAG-1 and to a model based on fuzzy set theory in the case of CADIAG-2. In both systems two kinds of relationships between medical entities are considered: (1) necessity of occurrence and (2) sufficiency of occurrence. Statistical interpretations using the 2 X 2 table paradigm yield a way to calculate these relationships automatically from samples of patient data. Results obtained by exploiting 3530 patient records from a rheumatological hospital are presented. The described application is a machine-learning program that allows inductive learning from examples under statistical uncertainty.