Physical Sciences and Mathematics Commons^™

Orders On Intervals Over Partially Ordered Sets: Extending Allen's Algebra And Interval Graph Results, Francisco Zapata, Vladik Kreinovich, Cliff Joslyn, Emilie Hogan

Departmental Technical Reports (CS)

To make a decision, we need to compare the values of quantities. In many practical situations, we know the values with interval uncertainty. In such situations, we need to compare intervals. Allen's algebra describes all possible relations between intervals on the real line which are generated by the ordering of endpoints; ordering relations between such intervals have also been well studied. In this paper, we extend this description to intervals in an arbitrary partially ordered set (poset). In particular, we explicitly describe ordering relations between intervals that generalize relation between points. As auxiliary results, we provide a logical interpretation of …