# Allen's Interval Calculus

 Title: Allen's Interval Calculus Author: Fadoua Ghourabi Submission date: 2016-09-29 Abstract: Allen’s 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 832–843, 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 (IJCAI’85), pages 528–531, 1985. BibTeX: @article{Allen_Calculus-AFP, author = {Fadoua Ghourabi}, title = {Allen's Interval Calculus}, journal = {Archive of Formal Proofs}, month = sep, year = 2016, note = {\url{https://isa-afp.org/entries/Allen_Calculus.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.