Topological augmentation: A step forward for qualitative partition reasoning

Abstract

The current state of the art for partition based qualitative spatial reasoning systems such as the 9-intersection, 9+-intersection, direction relation matrix, and peripheral direction relations is that of the binary set intersection — either empty or non-empty — conveying the intersection (or lack thereof) of an object in the sets deriving the partition. While such representations are sufficient for topological components of objects, these representations are not sufficient for various tasks in qualitative spatial reasoning (composition, representation transfer, converse, etc.) regarding partitions as tiles. Topological augmentation expands the current binary status quo into a system of assigning topological relations between objects and tiles. A case study is presented in the form of the direction relation matrix, demonstrating that an increased vocabulary has benefits for spatial information systems, providing localized context within a qualitative embedding.