Abstract: 
We introduce a theory of temporal logic operators using sets of natural numbers as time domain, formalized in a shallow embedding manner. The theory comprises special natural intervals (theory IL_Interval: open and closed intervals, continuous and modulo intervals, interval traversing results), operators for shifting intervals to left/right on the number axis as well as expanding/contracting intervals by constant factors (theory IL_IntervalOperators.thy), and ultimately definitions and results for unary and binary temporal operators on arbitrary natural sets (theory IL_TemporalOperators). 
BibTeX: 
@article{NatIntervalLogicAFP,
author = {David Trachtenherz},
title = {Interval Temporal Logic on Natural Numbers},
journal = {Archive of Formal Proofs},
month = feb,
year = 2011,
note = {\url{http://isaafp.org/entries/NatIntervalLogic.html},
Formal proof development},
ISSN = {2150914x},
}
