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

  • Alexander Scivos
  • Bernhard Nebel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2205)


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.


languages of spatial relations spatial and temporal reasoning incomplete or imprecise spatial knowledge qualitative spatial reasoning constraint propagation ternary relation systems 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alexander Scivos
    • 1
  • Bernhard Nebel
    • 1
  1. 1.Institut für InformatikUniversität FreiburgFreiburgGermany

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