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On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi

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Spatial Information Theory (COSIT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9368))

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Abstract

Qualitative calculi play a central role in representing and reasoning about qualitative spatial and temporal knowledge. This paper studies distributive subalgebras of qualitative calculi, which are subalgebras in which (weak) composition distributives over nonempty intersections. The well-known subclass of convex interval relations is an example of distributive subalgebras. It has been proven for RCC5 and RCC8 that path consistent constraint network over a distributive subalgebra is always minimal and strongly n-consistent in a qualitative sense (weakly globally consistent). We show that the result also holds for the four popular qualitative calculi, i.e. Point Algebra, Interval Algebra, Cardinal Relation Algebra, and Rectangle Algebra. Moreover, this paper gives a characterisation of distributive subalgebras, which states that the intersection of a set of \(m\ge 3\) relations in the subalgebra is nonempty if and only if the intersection of every two of these relations is nonempty. We further compute and generate all maximal distributive subalgebras for those four qualitative calculi mentioned above. Lastly, we establish two nice properties which will play an important role in efficient reasoning with constraint networks involving a large number of variables.

Work supported by the Australian Research Council under DP120104159 and FT0990811.

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Notes

  1. 1.

    http://nuts.geovocab.org/.

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Authors and Affiliations

  1. Faculty of Engineering and Information Technology, Centre for Quantum Computation and Intelligent Systems, University of Technology Sydney, Sydney, Australia

    Zhiguo Long & Sanjiang Li

Authors
  1. Zhiguo Long
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  2. Sanjiang Li
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Correspondence to Sanjiang Li .

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Editors and Affiliations

  1. University of Zurich, Zurich, Switzerland

    Sara Irina Fabrikant

  2. ETH Zurich, Zurich, Switzerland

    Martin Raubal

  3. School of Computer Science and Informatics, University College Dublin, Dublin, Ireland

    Michela Bertolotto

  4. University of Winchester, Winchester, United Kingdom

    Clare Davies

  5. Dept. of Geography and Env. Studies, University of New Mexico, Albuquerque, New Mexico, USA

    Scott Freundschuh

  6. College of Arts and Science, University of Saskatchewan, Saskatoon, Canada

    Scott Bell

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Long, Z., Li, S. (2015). On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi. In: Fabrikant, S., Raubal, M., Bertolotto, M., Davies, C., Freundschuh, S., Bell, S. (eds) Spatial Information Theory. COSIT 2015. Lecture Notes in Computer Science(), vol 9368. Springer, Cham. https://doi.org/10.1007/978-3-319-23374-1_17

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  • DOI: https://doi.org/10.1007/978-3-319-23374-1_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23373-4

  • Online ISBN: 978-3-319-23374-1

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