The Unified Modeling Language UML is a language for specifying, visualizing and documenting object-oriented systems. UML combines the concepts of OOA/OOD, OMT and OOSE and is intended as a standard in the domain of object-oriented analysis and design. Due to the missing formal, mathematical foundation of UML the syntax and the semantics of a number of UML constructs are not precisely defined. This paper outlines a proposal for the formal foundation of UML that is based on a mathematical system model.