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Publication type: Article
Author: Till Mossakowski, Reinhard Moratz, Dominik Lücke
Title: Relations Between Spatial Calculi About Directions and Orientations
Journal: Journal of Artificial Intelligence Research
Abstract: Qualitative spatial descriptions characterize essential properties of spatial objects or configurations by typically relying on relative comparisons rather than measuring. Typically, in qualitative approaches only relatively coarse distinctions between configurations are made. Qualitative spatial knowledge can be used to represent incomplete and underdetermined knowledge in a systematic way. This is especially useful if the task is to describe features of classes of configurations rather than individual configurations.

Relative directions play a key role in human spatial descriptions and there are several approaches how to represent them using qualitative methods. In these approaches directions between spatial locations can be expressed as constraints over infinite domains, e.g. the Euclidean plane. The theory of relation algebras has been successfully applied to this field. Viewing relation algebras as universal algebras and applying standard tools from universal algebra in this work, we (re)define notions of qualitative constraint calculus, of homomorphism between these, and of quotient of these. Based on this method we derive important properties for spatial calculi from corresponding properties of related calculi. From a conceptual point of view these formal mappings between calculi are a means to translate between different granularities.
PDF Version: http://iws.cs.uni-magdeburg.de/~mossakow/papers/RelBetwSpatCalc.pdf
Keywords: Qualitative Spatial Reasoning Universal Algebra
Status: Reviewed
Last updated: 09. 02. 2015

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