Orders on Intervals Over Partially Ordered Sets: Extending Allen's Algebra and Interval Graph Results

Authors

Francisco Zapata, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Cliff Joslyn, National Security Directorate Pacific Northwest National LaboratoryFollow
Emilie Hogan, Fundamental and Computational Sciences Directorate Pacific Northwest National LaboratoryFollow

Publication Date

8-2012

Comments

Technical Report: UTEP-CS-12-09b

Abstract

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 the relation between intervals, and extend the results about interval graphs to intervals over posets.