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Double-Crossing: Decidability and Computational Complexity of a Qualitative Calculus for Navigation

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Spatial Information Theory (COSIT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2205))

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Abstract

The Double Cross calculus has been proposed for the purpose of navigation based on qualitative information about spatial configurations. Up until now, however, no results about algorithmic properties of this calculus are known. First, we explore the possibility of applying constraint propagation techniques to solve the reasoning problem in this calculus. For this purpose, we have to generalize the known techniques for binary relations because the Double Cross calculus is based on ternary relations. We will show, however, that such a generalization leads to problems. The Double Cross calculus is not closed under composition and permutation. Further, as we will show, there exists no finite refinement of the base relations with such a closure property. Finally, we show that determining satisfiability of constraint systems over Double Cross relations is NP-hard, even if only the base relations of the Double Cross calculus are used. On the positive side, however, we show that the reasoning problem is solvable in PSPACE.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Freiburg, Georges-Köhler-Allee, Geb. 52, D-79110, Freiburg, Germany

    Alexander Scivos & Bernhard Nebel

Authors
  1. Alexander Scivos
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  2. Bernhard Nebel
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Editor information

Editors and Affiliations

  1. Department of Geography, University of California, Santa Barbara, CA, 93106, USA

    Daniel R. Montello

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Scivos, A., Nebel, B. (2001). Double-Crossing: Decidability and Computational Complexity of a Qualitative Calculus for Navigation. In: Montello, D.R. (eds) Spatial Information Theory. COSIT 2001. Lecture Notes in Computer Science, vol 2205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45424-1_29

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  • DOI: https://doi.org/10.1007/3-540-45424-1_29

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  • Print ISBN: 978-3-540-42613-4

  • Online ISBN: 978-3-540-45424-3

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