A graded approach to directions between extended objects

Abstract

In this paper, we present the concept of graded sections, which allows us to compare alternative conceptualizations of direction relations and to process them in an integrative manner. To describe graded sections, section bundles are introduced, which provide formal means to (1) compare alternative candidates that are related via a direction relation like “north” or “south-east,” (2) distinguish between good and not so good candidates, and (3) select a best candidate. The concepts and methods are exemplified with the cardinal direction “north,” however, they are applicable to all cardinal directions, including the “cyclical east–west” and other directional terms, such as “left” and “in front of.”.