In this paper we argue for the importance of doing inference over the information expressed by the annotations of temporally annotated corpora. We describe the process of inferential closure which can be applied to determine the full temporal content that follows from an annotation. We illustrate the importance of temporal inference and temporal closure in relation to three tasks, which are: (a) the comparison of different temporal annotations, (b) facilitating the manual annotation process needed to create temporally annotated corpora and (c) empirical investigations done over temporally annotated data.