Expressiveness of Metric modalities for continuous time

Details Expressiveness of Metric modalities for continuous time Expressiveness of Metric modalities for continuous time

2006-11-22

arxiv.org/abs/cs/0611119v2

LMCS 3 (1:3) 2007

Computer Science

Logic in Computer Science

Scientific paper

10.2168/LMCS-3(1:3)2007

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.

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