Partial order Semantics of Sequence Diagrams for Mobility.

There exist different formalism for mobile system specification, but until very recently, there was no satisfactory graphical notation for modelling of such systems. In a previous paper, we have introduced the so-called Sequence Diagrams for Mobility (SDM), a graphical notations based on UML Sequence Diagram. This notation has been used in several case studies and proved very useful. In this paper we introduce a formal, partial order based semantics for SDM. We define the notion of run and show how to figure out the system topology from the information contained in a run. We formalize the zoom-out abstraction mechanism introduced in a previous paper and show that its application does not depend on the particular order it is applied. We formalise also the notion of lifeline introduced informally in the previous paper. We integrate our semantics with UML2.0 and show that they fit well together. We explain our approach using series of examples.