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 [D03], 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 [HRS98], 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 [AFH96] is expressively complete with respect to an MSO corresponding to an appropriate set of input-determined operators.