This article surveys the linear temporal logic (LTL) literature and presents all the LTL theorems from the survey, plus many new ones, in a calculational deductive system. Calculational deductive systems, developed by Dijkstra and Scholten and extended by Gries and Schneider, are based on only four inference rules—Substitution, Leibniz, Equanimity, and Transitivity. Inference rules in the older Hilbert-style systems, notably modus ponens, appear as theorems in this calculational deductive system. This article extends the calculational deductive system of Gries and Schneider to LTL, using only the same four inference rules. Although space limitations preclude giving a proof of every theorem in this article, every theorem has been proved with calculational logic.

中文翻译：

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一种线性时序逻辑的计算演绎系统

本文调查了线性时序逻辑 (LTL) 文献，并在计算演绎系统中介绍了调查中的所有 LTL 定理，以及许多新定理。由 Dijkstra 和 Scholten 开发并由 Gries 和 Schneider 扩展的计算演绎系统仅基于四个推理规则——替代、莱布尼茨、平等和传递性。较早的希尔伯特式系统中的推理规则，尤其是前件式，在这个计算演绎系统中作为定理出现。本文将 Gries 和 Schneider 的计算演绎系统扩展到 LTL，仅使用相同的四个推理规则。尽管篇幅限制无法证明本文中的每个定理，但每个定理都已用计算逻辑进行了证明。