  Temporal logics (TLs) have been widely used to formalize interpretable tasks
for cyber-physical systems. Time Window Temporal Logic (TWTL) has been recently
proposed as a specification language for dynamical systems. In particular, it
can easily express robotic tasks, and it allows for efficient, automata-based
verification and synthesis of control policies for such systems. In this paper,
we define two quantitative semantics for this logic, and two corresponding
monitoring algorithms, which allow for real-time quantification of satisfaction
of formulas by trajectories of discrete-time systems. We demonstrate the new
semantics and their runtime monitors on numerical examples.
