Allen's Hourglass: Probabilistic Treatment of Interval Relations

The paper is motivated by the need to handle robustly the uncertainty of temporal intervals, e.g. as it occurs in automated event detection in video streams. The paper introduces a two-dimensional mapping of Allen's relations, based on orthogonal characteristics of interval relations, namely relative position and relative size. The hourglass-shaped mapping also represents limit cases that correspond to durationless intervals. Based on this mapping, we define two sets of primitive interval relations in terms of the relative positioning and relative size of intervals. These primitives are then used to derive a probabilistic set of Allen's relations. A number of example cases are presented to illustrate how the proposed approach can improve the robustness of interval relations.