On the expressiveness and monitoring of Metric Temporal Logic

Hsi-Ming Ho, Joël Ouaknine, and James Worrell

It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<,+1]) when interpreted over timed words; this remains true even when the time domain is bounded a priori. In this work, we present an extension of MTL with the same expressive power as FO[<,+1] over bounded timed words (and also, trivially, over time-bounded signals). We then show that expressive completeness also holds in the general (time-unbounded) case if we allow the use of rational constants q ∈ Q in formulas. This extended version of MTL therefore yields a definitive real-time analogue of Kamp's theorem. As an application, we propose a trace-length independent monitoring procedure for our extension of MTL, the first such procedure in a dense real-time setting.

Logical Methods in Computer Science 15(2), 2019. 52 pages.

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