Temporal reasoning with aspectual adverbs

Our central aim is to account for the validity of reasoning patterns involving focus adverbs in contexts where the temporal reference point may change during the process of interpretation of the premises. This paper proposes a dynamic semantics of such temporal inferences, determining what is updated in the interpretation and what information is preserved. In order to capture the various informational dimensions involved in this dynamic reasoning a basic polarity grid is proposed, generalizing the distinction between positive and negative polarity of event-types. Corresponding to this polarity grid, a binary bit-string calculus is introduced, which is three-dimensional for ordinary aspectual adverbs, but five-dimensional for focus aspectual adverbs. This calculus serves first to characterize valid static temporal reasoning, i.e. inferences which concern one and the same information state. Valid dynamic temporal reasoning across changing contexts or information states is subsequently characterized by polarity reversal operations in this calculus.