I argue that an action-based model of belief update is largely compatible with the proposals advanced in the literature on formal approaches to discourse interpretation, especially the recent work by Asher and Kamp, yet allows for a close integration between the processestracking the attentional state and performing intention recognition. In addition, I show that this kind of model, once augmented with a more expressive representation for events and situations, affords a formalization of phenomena like discourse segmentation and focus shift. The logic presented in the paper, besides allowing reasoning about the way conversational events group in conversational threads, is also appropriate as a target of a formal translation procedure, so that a discourse interpretation procedure alternative to the DRS construction algorithm can be specified.