  We consider a general notion of timed automata with input-determined guards
and show that they admit a robust logical framework along the lines of [D
'Souza03], in terms of a monadic second order logic characterisation and an
expressively complete timed temporal logic. We then generalize these automata
using the notion of recursive operators introduced by Henzinger, Raskin, and
Schobbens, and show that they admit a similar logical framework. These results
hold in the ``pointwise'' semantics. We finally use this framework to show that
the real-time logic MITL of Alur et al is expressively complete with respect to
an MSO corresponding to an appropriate input-determined operator.
