  Labeled continuous-time Markov chains (CTMCs) describe processes subject to
random timing and partial observability. In applications such as runtime
monitoring, we must incorporate past observations. The timing of these
observations matters but may be uncertain. Thus, we consider a setting in which
we are given a sequence of imprecisely timed labels called the evidence. The
problem is to compute reachability probabilities, which we condition on this
evidence. Our key contribution is a method that solves this problem by
unfolding the CTMC states over all possible timings for the evidence. We
formalize this unfolding as a Markov decision process (MDP) in which each
timing for the evidence is reflected by a scheduler. This MDP has infinitely
many states and actions in general, making a direct analysis infeasible. Thus,
we abstract the continuous MDP into a finite interval MDP (iMDP) and develop an
iterative refinement scheme to upper-bound conditional probabilities in the
CTMC. We show the feasibility of our method on several numerical benchmarks and
discuss key challenges to further enhance the performance.
