Dynamics of a Nearness Relation—First Results

The system of administrative units for a state like Switzerland can be formally described by a totally ordered set of nested partitions where, e.g., the municipalities make up a finer partition than the partition induced by districts. Based on these partitions one can define binary non-symmetric nearness relations between regions in which the second argument determines the granularity (or the scaling level) w.r.t. which the first-argument region is to be considered near or not. The logical properties of such nearness relations, especially w.r.t. their relation to proximity relations, have been worked out in the authors’ contribution to ECAI 2012. Referring to these properties, in this paper we extend the investigation to the dynamics of the nearness relation. In particular, we investigate how a change within the total order of partitions (e.g., two municipalities are merged) affects the induced nearness relation.