Qualitative Spatial Reasoning Using Real Algebraic Geometry

Commonsense reasoning is a major challenge in Artificial Intelligence (AI). As qualitative descriptions comprise a great deal of our everyday language, commonsense reasoning is concerned with developing and processing such qualitative representations. This applies especially to commonsense reasoning about space, where spatial objects are in particular characterized by their spatial relations to each other. Consequently, to endow spatial assistance systems, such as geographic information systems or computer-aided design, a thorough understanding of qualitative spatial relations is required. Qualitative Spatial Reasoning (QSR), a subfield of AI, approaches this very challenge [CR08]. QSR aims at providing calculi which allow a machine to represent and reason with spatial relations using a finite set of symbols. Among many spatial aspects handled in QSR, topological and orientation information have been extensively researched. However, whereas there is a comprehensive treatise on reasoning with topological information [Ren02], reasoning about orientation information is still an unexplored area. There neither exists a precise understanding of reasoning complexity, nor a sound and complete method has been proposed to tackle QSR reasoning problems. This is a challenge when integrating geospatial information is considered, since orientation information is ubiquitous in geographic space.