Expressiveness of metric modalities for continuous time

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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.

Original languageEnglish
Article number3
JournalLogical Methods in Computer Science
Issue number1
StatePublished - 23 Feb 2007


  • Expressive completeness
  • Real Time
  • Temporal Logics


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