Spatial Reasoning

Origins of the Field of Spatial Reasoning

The study of spatial reasoning dates back to ancient times. It is known that the Egyptians used a variety of [Page 427]systematic procedures for spatial inference, especially with regard to measuring and demarcating areas of land. Geometry (literally, “earth measurement”) was also a central topic of ancient Greek mathematics. This investigation culminated in the publication (around 300 BC) of Euclid's Elements, an axiomatic system that provides a more or less comprehensive set of rules for reasoning about geometrical figures as described by points and lines and the relationships between them.

A major shift in the analysis and representation of spatial information was instigated by Descartes (1596–1650), who showed how point locations in space can be represented by means of numerical coordinates. This idea can be generalized to specify complex figures in terms of sets of numerical values and equations. The coordinate-based approach provides an extremely powerful mathematical tool for representing and manipulating spatial information and enables certain useful kinds of spatial reasoning to be carried out by algebraic numerical methods. Consequently, the spatial representations used in modern scientific models and computational information systems (such as GIS) are predominantly Cartesian in nature.

Although the Cartesian analysis of space is both profoundly illuminating and of immense practical value, it does have limitations and is ill-suited to describing many intuitively natural forms of spatial inference. The main limitation stems from the fact that concise and mathematically simple descriptions of coordinates can be given only for specific instances of spatial figures and configurations whose geometry is fully determined, whereas natural reasoning about space is often couched in terms of general qualitative properties and relationships of spatial objects. For instance, we may know that a spatial region is convex or that one spatial region is part of another, without knowing the particular geometry of the regions involved. Qualitative reasoning is required whenever spatial information is partial or is presented in terms of abstract high-level concepts.

Recently, arising out of the Knowledge Representation strand of Artificial Intelligence (AI) and also from the need for more flexible interaction with GIS, much research has been directed toward the study of reasoning with qualitative spatial information. The field of qualitative spatial reasoning is now an established branch of AI research, and elements of this work are beginning to be incorporated into GIS.

Elements and Subdomains of Spatial Information

The realm of spatial information encompasses a wide variety of different entities, properties, and relationships. Because reasoning with all these aspects together is extremely complex, representations designed for computing spatial inferences typically handle only subdomains of spatial information, consisting of specific types of entities and a limited range of related concepts. This section summarizes the most significant ways in which the domain of spatial information can be divided into more restricted subdomains.

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