Computational approaches to discourse understanding have a two-part goal: (1) to identify those aspects of discourse understanding that require process-based accounts, and (2)to characterize the processes and data structures they involve. To date, in the area of reference, process-based accounts have been developed for subsequent reference via anaphoric pronouns and reference via definite descriptors. In this paper, I propose and argue for a process-based account of subsequent reference via deictic expressions. A significant feature of this account if that it attributes distinct mental reality to units of text often called discourse segments, a reality that is distinct from that of the entities described therein.