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A Representation Theorem for Spatial Relations

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AI 2015: Advances in Artificial Intelligence (AI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9457))

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Abstract

Spatial relations have been investigated in various inter-related areas such as qualitative spatial reasoning (for agents moving in an environment), geographic information science, general topology, and others. Most of the results are specific constructions of spatial relations that fulfill some required properties. Results on setting up axioms that capture the desired properties of the relations are rare. And results that characterize spatial relations in the sense that they give a complete set of axioms for the intended spatial relations still have to be presented. This paper aims at filling the gap by providing a representation theorem: It shows that there is a finite set of axioms that are fulfilled by a binary relation if and only if it can be constructed as a binary spatial relation based on a nested partition chain.

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Notes

  1. 1.

    An extended version of this paper with all proofs can be found at the following URL: https://dl.dropboxusercontent.com/u/65078815/AI15representation.pdf.

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Author information

Authors and Affiliations

  1. Institute of Information Systems (IFIS), University of Lübeck, Lübeck, Germany

    Özgür Lütfü Özçep

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  1. Özgür Lütfü Özçep
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Correspondence to Özgür Lütfü Özçep .

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Editors and Affiliations

  1. The University of Waikato, Hamilton, New Zealand

    Bernhard Pfahringer

  2. The Australian National University, Canberra, Aust Capital Terr, Australia

    Jochen Renz

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Özçep, Ö.L. (2015). A Representation Theorem for Spatial Relations. In: Pfahringer, B., Renz, J. (eds) AI 2015: Advances in Artificial Intelligence. AI 2015. Lecture Notes in Computer Science(), vol 9457. Springer, Cham. https://doi.org/10.1007/978-3-319-26350-2_39

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  • DOI: https://doi.org/10.1007/978-3-319-26350-2_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26349-6

  • Online ISBN: 978-3-319-26350-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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