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The Galois lattice as a hierarchical structure for topological relations

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Abstract

This paper presents the construction and the comparison of Galois lattices of topological relations for qualitative spatial representation and reasoning. The lattices rely on a correspondence between computational operations working on quantitative data, on the one hand, and topological relations working on qualitative knowledge units, on the other hand. After introducing the context of the present research work, i.e. the RCC-8 model of topological relations, we present computational operations for checking topological relations on spatial regions. From these operations are derived two sets of computational conditions that can be associated to topological relations through a Galois connection. The associated Galois lattices are presented and compared. Elements on the practical use of the lattices for representing spatial knowledge and for reasoning are also introduced and discussed.

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Authors and Affiliations

  1. LORIA – UMR 7503, BP 239, 54506, Vandœuvre-lès-Nancy, France

    Amedeo Napoli & Florence Le Ber

  2. CEVH, ENGEES, 1, Quai Koch, 67000, Strasbourg, France

    Florence Le Ber

Authors
  1. Amedeo Napoli
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  2. Florence Le Ber
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Correspondence to Florence Le Ber.

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Napoli, A., Le Ber, F. The Galois lattice as a hierarchical structure for topological relations. Ann Math Artif Intell 49, 171–190 (2007). https://doi.org/10.1007/s10472-007-9054-5

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  • DOI: https://doi.org/10.1007/s10472-007-9054-5

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