On the Robustness of Qualitative Distance- and Direction-Reasoning*

This paper focuses on spatial information derived from the composition of two pairs of cardinal directions (e.g., North and North-East) and approximate distances (e.g., near and far), i.e., given the approximate distances a1 (A, B) and a2 (B, C) and the cardinal directions c1 (A, B) and c2 (B, C), what are a3 (A, C) and c3 (A, C)? Spatial reasoning about cardinal directions and approximate distances is challenging because distance and direction will affect the composition. This paper investigates the dependency between qualitative and quantitative inference methods for reasoning about cardinal directions and approximate distances. Cardinal directions are based on a 4-sector model (North, East, South, West), while approximate distance correspond to a set of ordered intervals that provide a complete partition (non-overlapping and mutually exclusive) such that the following interval is greater than or equal to the previous one (for example, “far” would * This work was partially supported through the NCGIA by NSF grant No. SES-8810917. Additionally, Max Egenhofer’s work is also supported by NSF grant No. IRI-9309230, a grant from Intergraph Corporation, and the Scientific Division of the North Atlantic Treaty Organization. Jung-Hong Hong’s work was partially supported by a University of Maine International Student Tuition Waiver. Andrew Frank’s work is partially supported by a grant from Intergraph Corporation. Proceedings of Autocarto 12, D. Peuquet (Ed.), Charlotte, NC, February 1995. extend over a distance that is at least as great as “medium.”) We ran comprehensive simulations of quantitative reasoning, and compared the results with the ones obtained from quantitative reasoning. The results indicate that the composition is robust if the ratio between two consecutive intervals of quantitative distances is greater than 3.