Expressiveness of Metric modalities for continuous time
<|reference_start|>Expressiveness of Metric modalities for continuous time: We prove a conjecture by A. Pnueli and strengthen it showing a sequence of "counting modalities" none of which is expressible in the temporal logic generated by the previous modalities, over the real line, or over the positive reals. Moreover, there is no finite temporal logic that can express all of them over the real line, so that no finite metric temporal logic is expressively complete.<|reference_end|>
@article{hirshfeld2006expressiveness,
    title={Expressiveness of Metric modalities for continuous time},
    author={Yoram Hirshfeld and Alexander Rabinovich},
    journal={Logical Methods in Computer Science, Volume 3, Issue 1 (February
  23, 2007) lmcs:2225},
    year={2006},
    doi={10.2168/LMCS-3(1:3)2007},
    archivePrefix={arXiv},
    eprint={cs/0611119},
    primaryClass={cs.LO}
}