The Galois lattice as a hierarchical structure for topological relations

Amedeo Napoli 1 Florence Le Ber 1, 2
1 ORPAILLEUR - Knowledge representation, reasonning
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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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Submitted on : Thursday, July 12, 2007 - 3:48:29 PM
Last modification on : Thursday, January 11, 2018 - 6:19:54 AM

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Amedeo Napoli, Florence Le Ber. The Galois lattice as a hierarchical structure for topological relations. Annals of Mathematics and Artificial Intelligence, Springer Verlag, 2007, pp.1-20. ⟨10.1007/s10472-007-9054-5⟩. ⟨hal-00162171⟩



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