Instantiation Semantics for Message Sequence Charts

Message Sequence Charts (MSCs) is a standardized visual notation for expressing requirements in communicating systems. MSCs are commonly used to specify scenarios describing message exchange among entities such as objects, components, systems, etc. A multiplicity is a modeling construct that is used to define constraints in the existential relationships between entities and it is frequently found in static models, such as class or entity diagrams. This paper describes a formal approach for formalizing the combination of MSCs with multiplicities. The formalization is achieved by defining an instantiation partial function that provides a clear interpretation of how to instantiate MSCs with multiplicities. The formalization uses composition operators that are used to formalize inline expressions (a well-known MSCs modeling construct). This formalization is designed to allow integration with the current formal semantics proposed for MSCs