Defining semantics for UML is a difficult task. Disagreements in the meaning of UML constructs as well as the size of UML are major obstacles. In this report, we describe our approach to define the semantics for UML. Semantics is defined denotationally as a mapping into our semantics domain called the system model [4, 5, 6]. We demonstrate our approach by defining the semantics for a comprehensive version of class diagrams. The semantics definition is detailed for UML/P class diagrams, a variant of class diagrams which restricts the use of a few methodologically and semantically involved concepts. Class diagrams are well-known and rather easy to understand and thus perfect to examine the usability of the system model for precise semantic mappings.