Metric Temporal Logic with Durations

We present a formal framework based on metric temporal logic (MTL) for specifying and verifying real-time systems with a continuous environment. Metric temporal logic is extended to allow speciication of properties about duration of system's states. We prove that every formula of the duration calculus (DC) can be translated into an equivalent MTL-R formula. Expressiveness of DC and MTL-R are compared. We formulate axioms for MTL-R and a sound rule for proving duration properties of timed transition systems.