A Sound Observational Semantics for Modal Transition Systems

Modal Transition Systems (MTS) are an extension of Labelled Transition Systems (LTS) that distinguish between required, proscribed and unknown behaviour and come equipped with a notion of refinement that supports incremental modelling where unknown behaviour is iteratively elaborated into required or proscribed behaviour. The original formulation of MTS introduces two alternative semantics for MTS, strong and weak, which require MTS models to have the same communicating alphabet, the latter allowing the use of a distinguished unobservable action. In this paper we show that the requirement of fixing the alphabet for MTS semantics and the treatment of observable actions are limiting if MTS are to support incremental elaboration of partial behaviour models. We present a novel semantics, branching alphabet semantics, for MTS inspired by branching LTS equivalence, we show that some unintuitive refinements allowed by weak semantics are avoided, and prove a number of theorems that relate branching refinement with alphabet refinement and consistency. These theorems, which do not hold for other semantics, support the argument for considering branching implementation of MTS as the basis for a sound semantics to support behaviour model elaboration.