A Logical Approach to Represent and Reason about Calendars

In this paper, we propose a logical approach to represent and reason about different time granularities. We identify a time granularity as a discrete infinite sequence of time points properly labelled with proposition symbols marking the starting and ending points of the corresponding granules, and we intensively model sets of granularities with linear time logic formulas. Some real-world granularities are provided, to motivate and exemplify our approach. The proposed framework permits to algorithmically solve the consistency, the equivalence, and the classification problems in a uniform way, by reducing them to the validity problem for the considered linear time logic.