Positive and Negative Results on the Decidability of the Model-Checking Problem for an Epistemic Extension of Timed CTL

We present TCTLK, a continuous-time variant of the Computational Tree Logic with knowledge operators, generalizing both TCTL, the continuous-time variant of CTL, and CTLK, the epistemic generalization of CTL.Formulas are interpreted over timed automata, with a synchronous and perfect recall semantics,and the observability relation requires one to specify what clocks are visible for an agent.We show that, in general, the model-checking problem for TCTLK is undecidable, even if formulas do not use any clocks --and hence CTLK has an undecidable model-checking problem when interpreted over timed automata.On the other hand, we show that, when each agent can see all clock values,model-checking becomes decidable.