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In this paper we study several properties of the Exogenous Probabilistic Propositional Logic (EPPL ) , a logic for reasoning about probabilities, with the purpose of introducing a temporal version - Exogenous Probabilistic Linear Temporal Logic (EPLTL) . In detail, we give a small model theorem for EPPL and introduce a satisfaction and a model checking algorithm for both EPPL and EPLTL . We are also able to provide a (weakly) complete calculus for EPLTL . Finally, we conclude by pointing out some future work.