The representation of patient-specific information in the computer-based medical record requires an expressive formalism, which supports computational services particularly with respect to subsumption. These demands are not sufficiently met by conventional medical terminology and classification systems. This paper investigates the weaknesses of conventional systems, which are primarily coding systems and contain a certain amount of implicit knowledge. The alternatives are logic-based formalisms, particularly languages of the KL-ONE-family and conceptual graphs, which are based on the formal representation of meanings. Principles of these approaches are reported and compared to the concept representation language developed in the GALEN project. Finally, an overview on the BERNWARD model is given, which aims at the formal description, classification, and composition of medical concepts. In BERNWARD subsumption and part-whole relation are treated in a symmetrical manner. There are explicit and formal criteria for supporting the inference of generic and partitive relations.