Design and comparison of lattices of topological relations based on Galois lattice theory

Florence Le Ber (1) , Amedeo Napoli (1)

1 ORPAILLEUR - Knowledge representation, reasonning

This paper presents an approach to spatial representation and reasoning with lattices of topological relations. This approach is based on the Galois lattice theory that is used to create concepts, by associating sets of objects to sets of attributes. The objects considered here are the base relations of the region connection calculus RCC8 and the attributes are computational conditions that are used in geographic information systems for modeling topological relations. Three lattices, named TgE, TgL, and TgM, involving three sets of computational conditions, are introduced. The design and the properties of these lattices are detailed and then compared on the basis of the underlying computational conditions. Finally the three lattices are compared to each others, and to a fourth lattice, Tp, that is based on the set of all disjunctions of RCC8 relations, with respect to qualitative spatial reasoning capabilities.

Keywords: galois lattices; raisonnement spatial qualitatif; qualitative spatial reasoning; topological relations; relations topologiques; treillis de galois

Domains: Other [cs.OH]

Florence Le Ber, Amedeo Napoli. Design and comparison of lattices of topological relations based on Galois lattice theory. Eight International Conference on Principles of Knowledge Representation and Reasoning - KR'2002, Apr 2002, Toulouse, France, pp.37--46. ⟨inria-00100740⟩