Context: Activity Diagrams visualize sequences of instructions, including control flow. They are important and popular for modelling the dynamics of a (workflow) system. We address the problem of their unclear specifications. Problem: The semantics of Activity Diagrams is usually only given informally, e.g., in natural language, by means of concrete examples, via ontologies, or via some kind of operational semantics, usually limited to the flow of control only. For informal sketches in a discussion, this is okay. But as a vehicle for precise system specifications this is not sufficient. There exists no suitable mathematical, declarative semantics for Activity Diagrams in terms of state changes achieved. Research goal: To specify an unambiguous and mathematically sound declarative semantics for Activity Diagrams. Solution: Starting from the expressive class of well-formed Activity Diagrams defined earlier, we develop a declarative semantics for those Activity Diagrams in a syntax-driven way. Additional contribution: This novel idea and principles are generally applicable for other kinds of diagrams too, e.g., for Business Process Modeling diagrams.