Reasoning about Cardinal Directions Using Grids as Qualitative Geographic Coordinates

Abstract

In this article we propose a calculus of qualitative geographic coordinates which allows reasoning about cardinal directions on grid-based reference systems in maps. Grids in maps can be considered as absolute reference systems. The analysis reveals that the basic information coded in these reference systems is ordering information. Therefore, no metric information is required. We show that it is unnecessary to assume a coordinate system based on numbers in order to extract information like a point P is further north than a point Q. We investigate several grids in maps resulting from different types of projections. In addition, a detailed examination of the north arrow is given since it supplies a grid with ordering information. On this basis, we provide a general account on grids, their formalization and the inferences about cardinal directions drawn using qualitative geographic coordinates.

The research reported in this paper has been supported by the Deutsche Forschungsgemeinschaft (DFG) in the project ‘Axiomatik räumlicher Konzepte’ (Ha 1237-7) and ‘Räumliche Strukturen in Aspektkarten’ (Fr 806-8). We are in particular indebted to Carola Eschenbach and Christopher Habel for their valuable comments. This paper also benefits from fruitful discussions in the Hamburg Working Group on Spatial Cognition.