Reasoning about Cyclic Space: Axiomatic and Computational Aspects

  • Philippe Balbiani
  • Jean-François Condotta
  • Gérard Ligozat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2685)


In this paper we propose models of the axioms for linear and cyclic orders. First, we describe explicitly the relations between linear and cyclic models, from a logical point of view. The second part of the paper is concerned with qualitative constraints: we study the cyclic point algebra. This formalism is based on ternary relations which allow to express cyclic orientations. We give some results of complexity about the consistency problem in this formalism. The last part of the paper is devoted to conceptual spaces. The notion of a conceptual space is related to the complexity properties of temporal and spatial qualitative formalisms, including the cyclic point algebra.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Philippe Balbiani
    • 1
  • Jean-François Condotta
    • 2
  • Gérard Ligozat
    • 2
  1. 1.Institut de recherche en informatique de ToulouseToulouse Cedex 4France
  2. 2.Laboratoire d’informatique pour la mécanique et les sciences de l’ingénieurOrsay CedexFrance

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