Image-schemata-based spatial inferences: The container-surface algebra

Abstract

Algebras over spatial relations have become an important aspect of spatial reasoning for retrieving and handling large and complex spatial data sets. While such spatial relations play a fundamental role in specifying constraints in a spatial query language, there has been little concern as to whether existing spatial-relation algebras are cognitively plausible. In order to construct more intuitive and easier-to-use spatial query languages, this work pursues an alternative approach to spatial reasoning based on a small set of operators derived from concepts closely related to human thinking. The work focuses on a set of operators that are associated with the behavior of image schemata—recurrent patterns that people learn through bodily experiences and use for understanding the meaning of objects and situations. A study of a small-scale space, involving the surface and container schemata, describes objects in this space and the possible spatial relations among them. The informal description of these configurations are translated into a formal algebraic specification and generalized for spatial relations in a scene that involves surface and container schemata. This formalization axiomatizes spatial inferences that are then applied and compared to a larger geographic space. As a result, a small set of spatial operators are defined that apply to small- and large-scale spaces; however, these operators show discrepancies when applied to a combination of objects belonging to different scales. Interactive spatial query languages and spatial inference engines may be built on such basic spatial concepts as image schemata if they account for the differences in types, nature, and sizes of objects.