Metric spaces under interval uncertainty: Towards an adequate definition

Abstract

In many practical situations, we only know the bounds on the distances. A natural question is: knowing these bounds, can we check whether there exists a metric whose distance always lies within these bounds – or such a metric is not possible and thus, the bounds are inconsistent. In this paper, we provide an answer to this question. We also describe possible applications of this result to a description of opposite notions in commonsense reasoning.