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. We use this sequence to prove that over the real line there is no finite temporal logic that can express all the natural properties that arise when dealing with systems that evolve in continuous time.
['Yoram Hirshfeld', 'Alexander Rabinovich']
Expressiveness of metric modalities for continuous time