Representing and reasoning about temporal granularities

In this paper, we propose a new logical approach to represent and to reason about different time granularities. We identify a time granularity as an infinite sequence of time points properly labelled with proposition symbols marking the starting and ending points of the corresponding granules, and we symbolically model sets of granularities by means of linear time logic formulas. Some real-world granularities are provided, from a clinical domain and from the Gregorian Calendar, to motivate and exemplify our approach. Different formulas are introduced, which represent relations between different granularities. The proposed framework permits one 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.