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2008
Springer

Complexity of Metric Temporal Logics with Counting and the Pnueli Modalities

8 years 3 months ago
Complexity of Metric Temporal Logics with Counting and the Pnueli Modalities
The common metric temporal logics for continuous time were shown to be insufficient, when it was proved in [7, 12] that they cannot express a modality suggested by Pnueli. Moreover no temporal logic with a finite set of modalities can express all the natural generalizations of this modality. The temporal logic with counting modalities (TLC) is the extension of until-since temporal logic TL(U, S) by "counting modalities" Cn(X) and C n (n N); for each n the modality Cn(X) says that X will be true at least at n points in the next unit of time, and its dual C n(X) says that X has happened n times in the last unit of time. In [11] it was proved that this temporal logic is expressively complete for a natural decidable metric predicate logic. In particular the Pnueli modalities Pnk(X1, . . . , Xk), "there is an increasing sequence t1, . . . , tk of points in the unit interval ahead such that Xi holds at ti", are definable in TLC. In this paper we investigate the complexit...
Alexander Rabinovich
Added 26 Oct 2010
Updated 26 Oct 2010
Type Conference
Year 2008
Where FORMATS
Authors Alexander Rabinovich
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