Allen's interval algebra

For the type of boolean algebra called interval algebra, see Boolean algebra (structure)

Allen's interval algebra is a for temporal reasoning that was introduced by James F. Allen in 1983.

The calculus defines possible relations between time intervals and provides a composition table that can be used as a basis for reasoning about temporal descriptions of events.

The following 13 base relations capture the possible relations between two intervals.

${\displaystyle Y\,{\mathrel {\mathbf {>} }}\,X}$

${\displaystyle Y\,{\mathrel {\mathbf {mi} }}\,X}$

${\displaystyle Y\,{\mathrel {\mathbf {oi} }}\,X}$

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