In this paper, we show a new approach for reasoning about time and probability that combines a formal declarative language with a graph representation of systems of random variables for making inferences. First, we provide a continuous-time logic for expressing knowledge about time and probability. Then, we introduce the time net, a kind of Bayesian network for supporting inference with statements in the logic. Time nets encode the probability of facts and events over time. We provide a simulation algorithm to compute probabilities for answering queries about a time net. Finally, we consider an incremental probabilistic temporal database based on the logic and time nets to support temporal reasoning and planning applications. The result is an approach that is semantically well-founded, expressive, and practical.