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Continuous-time Markov decision processes (CTMDPs) are canonical models to express sequential decision-making under dense-time and stochastic environments. When the stochastic evolution of the environment is only available via sampling, model-free reinforcement learning (RL) is the algorithm-of-choice to compute optimal decision sequence. RL, on the other hand, requires the learning objective to be encoded as scalar reward signals. Since doing such transla- tions manually is both tedious and error-prone, a number of techniques have been proposed to translate high-level objec- tives (expressed in logic or automata formalism) to scalar re- wards for discrete-time Markov decision processes. Unfortu- nately, no automatic translation exists for CTMDPs. We consider CTMDP environments against the learning objectives expressed as omega-regular languages. Omega- regular languages generalize regular languages to infinite- horizon specifications and can express properties given in popular linear-time logic LTL. To accommodate the dense- time nature of CTMDPs, we consider two different semantics of omega-regular objectives: 1) satisfaction semantics where the goal of the learner is to maximize the probability of spend- ing positive time in the good states, and 2) expectation seman- tics where the goal of the learner is to optimize the long-run expected average time spent in the “good states” of the au- tomaton. We present an approach enabling correct translation to scalar reward signals that can be readily used by off-the- shelf RL algorithms for CTMDPs. We demonstrate the effec- tiveness of the proposed algorithms by evaluating it on some popular CTMDP benchmarks with omega-regular objectives.