Intervals, Points, and Branching Time

This paper extends Allen’s interval algebra to include points and either left or right-branching time. The branching time algebras each contain 24 relations: Allen’s original 13 relations, 5 more relations resulting from the inclusion of points, and 6 relations because of the inclusion of branching time. In this paper, I also present: (1) A technique for automatically deriving algebras of relations; (2) a new way of representing temporal constraint networks — the constraint matrix; and (3) a new way of performing constraint propagation — via constraint matrix multiplication.