# The Expressiveness of Metric Temporal Logic II: This time it's irrational!

Paul Hunter

- 11:30 13th June 2013 ( week 8, Trinity Term 2013 )051

In the first installment of "The Expressiveness of Metric Temporal
Logic" [1] we saw how Metric Temporal Logic (MTL) - an extension of
Linear Temporal Logic with timing constraints on the modal operators -
has the same expressive power as first order logic when the timing
constants are rational. In this talk we consider the case when
irrational constants can be used. We give a very succinct
characterization of precisely when MTL and FO have the same expressive
power which neatly generalizes several results in the area.

[1] For those that did not see the first talk there will be a brief recap of the results at the start of this talk.