Revisiting the expressiveness of metric temporal logic : A tale of "Je t'aime, moi non plus."

arXiv:2603.15379v4 Announce Type: replace Abstract: 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.