Towards an Integrated Graph Based Semantics for UML

Recently, we proposed an integrated formal semantics based on graph transformation for central aspects of UML class, object and state diagrams. In this paper, we explain the basic ideas of that approach and show how two more UML diagram types, sequence and collaboration diagrams, can be captured. For UML models consisting of a class diagram and particular state diagrams, a graph transformation system can be defined. Its graphs are associated with system states and its rules with operations in the class diagram and transitions in the state diagrams. Sequence and collaboration diagrams then characterize sequences of operation applications and therefore sequences of transformation rule applications. Thus valid sequence and collaboration diagrams correspond to derivations induced by the graph transformation system. Proceeding this way, it can be checked for example whether such an operation application sequence may be applied in a specific system state.