The expressiveness of Metric Temporal Logic (MTL) has been extensively studied throughout the last two decades. In particular, it has been shown that the \emph{interval-based} semantics of MTL is strictly more expressive than the \emph{pointwise} one. These results may suggest that enabling the evaluation of formulae at arbitrary time points \emph{instead of} positions of timed events increases the expressive power of MTL. In this paper, we formally argue otherwise. We demonstrate that under standard models of finite or non-Zeno infinite (action-based) timed executions, the interval-based and the pointwise semantics are incomparable. We then propose a new \emph{mixed} semantics that embeds both the pointwise and the interval-based ones.

翻译：度量时序逻辑（MTL）的表达性在过去二十年间得到了广泛研究。特别地，已有研究证明基于区间的MTL语义严格强于基于点的语义。这些结果可能暗示：允许在任意时间点（而非定时事件的位置）评估公式会增强MTL的表达能力。本文则提出相反的形式论证。我们证明，在有限或非Zeno无限（基于动作的）定时执行的标准模型下，基于区间与基于点的语义具有不可比性。进而提出一种融合了基于点与基于区间语义的新型混合语义。