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Furthermore, for <math>I=(a,b)</math> an interval, <math>x\in I</math> is considered as an abbreviation for <math>x>a\land x<b</math>; and similarly for every other kind of intervals.
The logic '''TPTL+Past'''<ref name="ExpressivenesOfTPTLAndMtl">{{cite journal |last1=Bouyer |first1=Patricia |author1-link=Patricia Bouyer-Decitre|last2=Chevalier |first2=Fabrice |last3=Markey |first3=Nicolas |title=On the Expressiveness of TPTL and MTL |journal=roceedings of the 25th Conference on Foundations of Software Technology and Theoretical Computer Science |date=2005 |page=436 |doi=10.1007/11590156_3 |url=https://hal.archives-ouvertes.fr/hal-01194615/document}}</ref> is built as the future fragment of '''TLS''' and also contains
* the temporal modal operator '''S'''.
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