Message sequence charts (MSCs) are a standardised formalismfor the specification of the system’s communication
behaviour that is widely used by industry. Various extensions to MSCs have recently been standardised by the
ITU. This paper treats the extension of MSCs with structural operators that allow the hierarchical composition of
MSCs. In particular, we propose a linear-time partial-order semantics for this extension that is based on the notion
of partial-order multi-sets (pomsets, for short). We provide a compositional denotational semantics for hierarchical
MSCs and show that well-known operations on pomsets correspond to the new composition operators in MSCs.
The main benefit of our approach is that the semantics is conceptually rather straightforward, as opposed to the
operational semantics for MSCs that is currently in the process of standardisation
