Qualitative Direction Calculi with Arbitrary Granularity

This paper proposes a generalization of previous approaches which enables qualitative calculi with an arbitrary level of granularity, so powerful that they can even emulate a quantitative representation based on a coordinate system.

Abstract

Binary direction relations between points in two-dimensional space are the basis to any qualitative direction calculus. Previous calculi are only on a very low level of granularity. In this paper we propose a generalization of previous approaches which enables qualitative calculi with an arbitrary level of granularity. The resulting calculi are so powerful that they can even emulate a quantitative representation based on a coordinate system. We also propose a less powerful, purely qualitative version of the generalized calculus. We identify tractable subsets of the generalized calculus and describe some applications for which these calculi are useful.