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A Substructural Modal Logic of Utility

机译：效用的子结构模态逻辑

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摘要

We introduce a substructural modal logic of utility that can be used to reason about optimality with respect to properties of states. Our notion of state is quite general, and is able to represent resource allocation problems in distributed systems. The underlying logic is a variant of the modal logic of bunched implications, and based on resource semantics, which is closely related to concurrent separation logic. We consider a labelled transition semantics and establish conditions under which Hennessy-Milner soundness and completeness hold. By considering notions of cost, strategy and utility, we are able to formulate characterizations of Pareto optimality, best responses, and Nash equilibrium within resource semantics. We also show that our logic is able to serve as a logic for a fully featured process algebra and explain the interaction between utility and the structure of processes.
机译：我们介绍了一种效用的子结构模态逻辑，该逻辑可用于推理关于状态属性的最优性。我们的状态概念相当笼统，并且能够表示分布式系统中的资源分配问题。基础逻辑是成束含义的模态逻辑的变体，并基于资源语义，该语义与并发分离逻辑密切相关。我们考虑标记的过渡语义，并建立轩尼诗-米尔纳健全性和完整性成立的条件。通过考虑成本，策略和效用的概念，我们能够在资源语义学范围内描述Pareto最优性，最佳响应和Nash均衡的特征。我们还表明，我们的逻辑能够用作功能齐全的过程代数的逻辑，并说明效用与过程结构之间的相互作用。

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