Hybrid dynamic logic institutions for event/data-based systems

Abstract

We propose varepsilon^downarrow(mathcal{vec{D}})-logic as a formal foundation for the specification anddevelopment of event-based systems with data states. The framework is presentedas an institution in the sense of Goguen and Burstall and the logic itself isparametrised by an underlying institution mathcal{vec{D}} whose structures are used tomodel data states. varepsilon^downarrow(mathcal{vec{D}})-logic is intended to cover a broad range ofabstraction levels from abstract requirements specifications up to constructivespecifications. It uses modal diamond and box operators over complex actionsadopted from dynamic logic. Atomic actions are pairs where e is an event and psi a state transition predicate capturing the allowedreactions to the event. To write concrete specifications of recursive processstructures we integrate (control) state variables and binders of hybrid logic.The semantic interpretation relies on event/data transition systems. For thepresentation of constructive specifications we propose operational event/dataspecifications allowing for familiar, diagrammatic representations by statetransition graphs. We show that varepsilon^downarrow(mathcal{vec{D}})-logic is powerful enough tocharacterise the semantics of an operational specification by a singlevarepsilon^downarrow(mathcal{vec{D}})-sentence. Thus the whole (formal) development process forevent/data-based systems relies on varepsilon^downarrow(mathcal{vec{D}})-logic and its semantics as a commonbasis. It is supported by a variety of implementation constructors which canexpress, among others, event refinement and parallel composition. Due to thegenericity of the approach, it is also possible to change a data stateinstitution during system development when needed. All steps of our formaltreatment are illustrated by a running example.