Representations of Topological Relations Between Simple Regions in Description Logics

Abstract

This paper proposes an operational approach to (1) formalize, in Description Logics (DL), the topological relations between simple regions and (2) automatically check whether a set of relations is consistent. The solution allows for the use of traditional DL reasoners (Pellet, Fact++, etc.) to check the consistency of relations and detect the sources of error. The solution does not require any specific extension of the DL or reasoner. The authors demonstrate how to apply this approach with Protégé and Fact++. Different spatial relations in agricultural and environmental applications are also provided to illustrate the possible uses of our method.

Homological relations: A methodology for the certification of irregular tessellations

“…Pioneered by Laurini and Milleret‐Raffort (1991), this idea is to list the geographic constraints a geographic object must follow. This track was continued by many researchers, among whom we can mention Plümer (1996), Cockcroft (1997), Servigne, Ubeda, Puricelli, and Laurini (2000), Bravo and Rodriguez (2009), Werder (2009), and Roussey, Pinet, and Schneider (2013), with the scope of establishing the list of spatial integrity constraints to detect errors and often visualize them for manual corrections. For instance, an integrity constraint can check whether a polygon is well formed (for instance, not having a butterfly shape) or if there is no overlay between two polygons.…”

Research in Agricultural and Environmental Information Systems

“…More recently, in 2013, the authors of Catherine Roussey, Pinet, and Schneider (2013) show how the ontology-based Description Logics (DL) can be used to model topological relations (Clementini & Di Felice, 1995;A. G. Cohn, B. Bennett, J. Gooday, & N. M. Gotts, 1997;Egenhofer, Clementini, & Di Felice, 1994) to check the consistency of these relations (Haarslev, Lutz, & Möller, 1998).…”