Allen's interval algebra
Allen's interval algebra is a calculus 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. Formal description Relations The following 13 base relations capture the possible relations between two intervals. Using this calculus, given facts can be formalized and then used for automatic reasoning. Relations between intervals are formalized as sets of base relations. The sentence During dinner, Peter reads the newspaper. Afterwards, he goes to bed. is formalized in Allen's Interval Algebra as follows: In general, the number of different relations between n intervals, starting with n = 0, is 1, 1, 13, 409, 23917, 2244361... OEIS A055203. The special case shown above is for n = 2. Composition of relations between intervals For reasoning about the relations between temporal intervals, Allen's interval algebra provides a composition table. Given the relation between and and the relation between and , the composition table allows for concluding about the relation between and . Together with a converse operation, this turns Allen's interval algebra into a relation algebra. For the example, one