Abstract

We propose ${\epsilon }^{\downarrow }(\overrightarrow{\mathcal{D}})$-logic as a formal foundation for the specification and development of event-based systems with data states. The framework is presented as an institution in the sense of Goguen and Burstall and the logic itself is parametrised by an underlying institution $\overrightarrow{\mathcal{D}}$ whose structures are used to model data states. ${\epsilon }^{\downarrow }(\overrightarrow{\mathcal{D}})$-logic is intended to cover a broad range of abstraction levels from abstract requirements specifications up to constructive specifications. It uses modal diamond and box operators over complex actions adopted from dynamic logic. Atomic actions are pairs [inline-graphic not available: see fulltext] 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. For the presentation of constructive specifications we propose operational event/data specifications allowing for familiar, diagrammatic representations by state transition graphs. We show that ${\epsilon }^{\downarrow }(\overrightarrow{\mathcal{D}})$-logic is powerful enough to characterise the semantics of an operational specification by a single ${\epsilon }^{\downarrow }(\overrightarrow{\mathcal{D}})$-sentence. Thus the whole (formal) development process for event/data-based systems relies on ${\epsilon }^{\downarrow }(\overrightarrow{\mathcal{D}})$-logic and its semantics as a common basis. It is supported by a variety of implementation constructors which can express, among others, event refinement and parallel composition. Due to the genericity of the approach, it is also possible to change a data state institution during system development when needed. All steps of our formal treatment are illustrated by a running example.

中文翻译：

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用于基于事件/数据的系统的混合动态逻辑机构

摘要

我们建议${\epsilon }^{\downarrow }(\overrightarrow{\mathcal{D}})$- 逻辑作为规范和开发具有数据状态的基于事件的系统的正式基础。该框架在 Goguen 和 Burstall 的意义上被呈现为一个机构，并且逻辑本身由一个基础机构参数化$\overrightarrow{\mathcal{D}}$其结构用于对数据状态进行建模。${\epsilon }^{\downarrow }(\overrightarrow{\mathcal{D}})$-logic 旨在涵盖从抽象需求规范到构造规范的广泛抽象级别。它在动态逻辑中采用的复杂动作上使用模态菱形和框运算符。原子动作是对 [inline-graphic not available: see fulltext] 其中e是一个事件和$\psi$一个状态转换谓词，捕获对事件的允许反应。为了编写递归过程结构的具体规范，我们集成（控制）状态变量和混合逻辑的绑定器。语义解释依赖于事件/数据转换系统。对于建设性规范的呈现，我们提出了操作事件/数据规范，允许通过状态转换图进行熟悉的图解表示。我们表明${\epsilon }^{\downarrow }(\overrightarrow{\mathcal{D}})$- 逻辑足够强大，可以通过单个 ${\epsilon }^{\downarrow }(\overrightarrow{\mathcal{D}})$-句子。因此，基于事件/数据的系统的整个（正式）开发过程依赖于${\epsilon }^{\downarrow }(\overrightarrow{\mathcal{D}})$- 逻辑和它的语义作为一个共同的基础。它由各种实现构造函数支持，其中可以表达事件细化和并行组合。由于该方法的通用性，还可以在系统开发过程中根据需要更改数据状态机构。我们正式处理的所有步骤都通过一个运行示例来说明。