A Hybrid Dynamic Logic for Event/Data-based Systems

TL;DR

This paper introduces $\ ext{\mathcal{E}^{\downarrow}}$-logic, a formal framework for specifying and developing event-based systems with local data states, integrating dynamic, hybrid, and operational semantics for comprehensive system modeling.

Contribution

The paper presents a novel logic that combines dynamic, hybrid, and operational features to specify event/data systems at various abstraction levels.

Findings

Logic can characterize operational specifications with a single sentence.

Supports refinement, parallel composition, and implementation constructors.

Provides diagrammatic and formal semantics for event/data systems.

Abstract

We propose $\mathcal{E}^{\downarrow}$-logic as a formal foundation for the specification and development of event-based systems with local data states. The logic is intended to cover a broad range of abstraction levels from abstract requirements specifications up to constructive specifications. Our logic uses diamond and box modalities over structured actions adopted from dynamic logic. Atomic actions are pairs $e /\psi$ where $e$ is an event and $\psi$ a state transition predicate capturing the allowed reactions to the event. To write concrete specifications of recursive process structures we integrate (control) state variables and binders of hybrid logic. The semantic interpretation relies on event/data transition systems; specification refinement is defined by model class inclusion. For the presentation of constructive specifications we propose operational event/data specifications allowing for familiar, diagrammatic representations by state transition graphs. We show that $\mathcal{E}^{\downarrow}$-logic is powerful enough to characterise the semantics of an operational specification by a single $\mathcal{E}^{\downarrow}$-sentence. Thus the whole development process can rely on $\mathcal{E}^{\downarrow}$-logic and its semantics as a common basis. This includes also a variety of implementation constructors to support, among others, event refinement and parallel composition.