# [isabelle] New in the AFP: Allen's Interval Calculus

Iâm happy to announce a new and rather unusual entry to the AFP: Allen's Interval Calculus, contributed by Fadoua Ghourabi:
> Allenâs interval calculus is a qualitative temporal representation of time events. Allen introduced 13 binary relations that describe all the possible arrangements between two events, i.e. intervals with non-zero finite length. The compositions are pertinent to reasoning about knowledge of time. In particular, a consistency problem of relation constraints is commonly solved with a guideline from these compositions. We formalize the relations together with an axiomatic system. We proof the validity of the 169 compositions of these relations. We also define nests as the sets of intervals that share a meeting point. We prove that nests give the ordering properties of points without introducing a new datatype for points. [1] J.F. Allen. Maintaining Knowledge about Temporal Intervals. In Commun. ACM, volume 26, pages 832â843, 1983. [2] J. F. Allen and P. J. Hayes. A Common-sense Theory of Time. In Proceedings of the 9th International Joint Conference on Artificial Intelligence (IJCAIâ85), pages 528â531, 1985.
You will find it here: https://www.isa-afp.org/entries/Allen_Calculus.shtml
Itâs great to see so much interesting and novel material flowing into the AFP!
Larry

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