Nowadays, with a growing use of location-aware, wirelessly connected, mobile devices, we can easily capture trajectories of mobile objects. To exploit these raw trajectories, we need to enhance them with semantic information. Several research fields are currently focusing on semantic trajectories to support queries and inferences to help users for validating and discovering more knowledge about mobile objects. The inference mechanism is needed for queries on semantic trajectories connected to other sources of information. Time and space knowledge are fundamental sources of information used by the inference operation on semantic trajectories. This article presents a case study of inference mechanism on semantic trajectories. We propose a solution based on an ontological approach for modelling semantic trajectories integrating time information and rules. We give experiments and evaluations of the proposed approach on generated and real data.