Again it's not only about time, but rather about space time, but quite different from the other mentioned approaches:

The Hungarian logicians Andreka, Madarasz, Nemeti, Toke and Sain have actually explored the possibilities of treating space-time and relativity in terms of model theory, so they really give axiomatizations in the technical sense and not just mathematical models. See the preprints on this page here, which include also a survey of previous axiomatizations of space-time.