We study translations from metric temporal logic (MTL) over the natural numbers to linear temporal logic (LTL). In particular, we present two approaches for translating from MTL to LTL which preserve the ExpSpace complexity of the satisfiability problem for MTL. In each of these approaches we consider the case where the mapping between states and time points is given by (i) a strict monotonic function and by (ii) a non-strict monotonic function (which allows multiple states to be mapped to the same time point). We use this logic to model examples from robotics, traffic management, and scheduling, discussing the effects of different modelling choices. Our translations allow us to utilise LTL solvers to solve satisfiability and we empirically compare the translations, showing in which cases one performs better than the other. We also define a branching-time version of the logic and provide translations into computation tree logic.

中文翻译：

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定理证明在自然上的逐点度量时间逻辑通过翻译

我们研究从自然数上的度量时间逻辑 (MTL) 到线性时间逻辑 (LTL) 的转换。特别是，我们提出了两种从 MTL 转换为 LTL 的方法，它们保留了 MTL 可满足性问题的 ExpSpace 复杂性。在这些方法中的每一种中，我们考虑状态和时间点之间的映射由（i）严格单调函数和（ii）非严格单调函数（允许多个状态映射到同一时间）给出的情况观点）。我们使用此逻辑对机器人、交通管理和调度的示例进行建模，并讨论不同建模选择的影响。我们的翻译允许我们利用 LTL 求解器来解决可满足性，我们凭经验比较翻译，显示在哪些情况下一个比另一个表现更好。