(PDF) Peter van Beek and Robin Cohen. Exact and approximate reasoning about temporal relations. Computational Intelligence 6:132-144, 1990.
Allen gives an algebra for representing qualitative temporal information about the relationships between pairs of intervals. In this paper, we address a fundamental reasoning task that arises in applications of the algebra: Given (possibly indefinite) knowledge about the relationships between intervals, find all feasible relationships between two intervals. We call this the minimal labels problem. Finding the minimal labels can be viewed as computing the deductive consequences of our knowledge. Determining exact solutions to this problem has been shown to be (almost assuredly) intractable. Allen gives an approximation algorithm based on constraint propagation. We present new approximation algorithms, determine analytically under what conditions the algorithms are exact, and examine, through some computational experiments, the quality of the approximate solutions produced by the algorithms. We also give a simple test for predicting when the approximation algorithms will and will not produce good quality approximations. Finally, we survey three example applications of the interval algebra chosen from the literature to show where the results of this paper could be useful.