### Citation

(PDF)
Peter van Beek and Robin Cohen.
Exact and approximate reasoning about temporal relations.
*Computational Intelligence*
6:132-144, 1990.

### Abstract

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.

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