Reasoning about Topological and Positional Information in Dynamic Settings

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Typical application fields of spatial and spatio-temporal representation formalisms and reasoning techniques include geographic information systems (GIS), mobile assistance systems for route finding, layout descriptions, and navigation tasks of robots interacting with humans. Often these formalisms focus on specific spatial aspects in that they use either topological or positional relations. In this paper we propose a formalism which allows for representing topological and positional relations between disks in the plane. Although this formalism employs a rather abstract representation of objects as disks, it provides an interesting test-bed for investigating typical problems that arise when topological and positional information about objects are combined, or when such combined formalisms are used to represent continuous changes in the considered application scenario.