Whenever humans refer to time, they do so with respect to a specific underlying calendar. So do most software applications. However, most theoretical models of time refer to time with respect to the integers (or reals). Thus, there is a mismatch between the theory and the application of temporal reasoning.

To lessen this gap, we propose a formal, theoretical definition of a calendar and show how one may specify dates, time points, time intervals, as well as sets of time points, in terms of constraints with respect to a given calendar. Furthermore, when multiple applications using different calendars wish to work together, there is a need to integrate those calendars together into a single, unified calendar. We show how this can be done. (Also cross-referenced as UMIACS-TR-97-12)