In systems modelling, a system typically comprises located resources relative to which processes execute. One important use of logic in informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their behaviour and properties. To this end, one requires an interpretation of logical formulae in terms of the resources and states of the system; such an interpretation is called a resource semantics of the logic. This paper shows how inferentialism -- the view that meaning is given in terms of inferential behaviour -- enables a versatile and expressive framework for resource semantics. Specifically, how inferentialism seamlessly incorporates the assertion-based approach of the logic of Bunched Implications, foundational in program verification (e.g., as the basis of Separation Logic), and the renowned number-of-uses reading of Linear Logic. This integration enables reasoning about shared and separated resources in intuitive and familiar ways, as well as about the composition and interfacing of system components.
翻译:在系统建模中,一个系统通常包含相对于进程执行的定位资源。逻辑在信息学中的一个重要用途是对此类系统进行建模,以便(可能通过自动化方式)推理其行为和属性。为此,需要根据系统的资源和状态对逻辑公式进行解释;这种解释被称为逻辑的资源语义学。本文展示了推理主义——即意义由推理行为赋予的观点——如何为资源语义学提供一种灵活且富有表现力的框架。具体而言,推理主义如何无缝整合基于断言的束合蕴含逻辑(该逻辑在程序验证中具有基础地位,例如作为分离逻辑的基础)以及线性逻辑中著名的使用次数解读。这一整合使得能够以直观且熟悉的方式推理共享和分离的资源,以及系统组件的组合与接口交互。