(PDF) Peter van Beek. Reasoning about qualitative temporal information. Artificial Intelligence 58:297-326, 1992. Preliminary versions of the paper appear in Proceedings of the 8th National Conference on Artificial Intelligence, Boston, Massachusetts, 728-734, July, 1990; and in Recent Advances in Qualitative Physics, Boi Faltings and Peter Struss (eds.), The MIT Press, 211-227, 1992.
Representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks. An interval-based framework and a point-based framework have been proposed for representing such temporal information. In this paper, we address two fundamental reasoning tasks that arise in applications of these frameworks: Given possibly indefinite and incomplete knowledge of the relationships between some intervals or points, (i) find a scenario that is consistent with the information provided, and (ii) find the feasible relations between all pairs of intervals or points. For the point-based framework and a restricted version of the interval-based framework, we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations. Our algorithms are marked improvements over the previously known algorithms. In particular, we develop an O(n^2) time algorithm for finding one consistent scenario that is an O(n) improvement over the previously known algorithm, where n is the number of intervals or points, and we develop an algorithm for finding all the feasible relations that is of far more practical use than the previously known algorithm. For the unrestricted version of the interval-based framework, finding a consistent scenario and finding the feasible relations have been shown to be NP-complete. We show how the results for the point algebra aid in the design of a backtracking algorithm for finding one consistent scenario that is shown to be useful in practice for planning problems.