Geographical Constrainst Revisited Through the Basic Relations of Contact, Share and Order

Robert Jeansoulin

In the framework of relation algebra and their use to represent space-time constraints, we present a constructive approach of a lattice of "topological constraints algebras" based upon three basic relations: contact, share and order, as tools to incrementally improve "discernibility". This scheme shows the articulations between Allen and RCC algebras, as well with intermediate and smaller algebras with 2, 3, 5 or 7 relations. Tractability values are estimated through the cardinaiity of convex and Ord-Horn classes for each of these algebras. We will discuss how models of geographic objects can be related to these algebras, in particular: notions of partitioning (districting) and of territory (no crisp borders). The main and original behind, is to exhibit a range of structures which enables us to choose the smaller that fit the model of objects associated to the application. For GIS applications, several extensions are proposed, to help the choice for some specific spatial problems: nested partitioning, river basin, cadastre changes.

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