On capturing first-order topological properties of planar spatial databases

Abstract

Spatial databases are modeled as closed semi-algebraic subsets of the real plane. First-order logic over the reals, expanded with a symbol to address the database, provides a natural language for expressing properties of such databases. Motivated by applications in geographical information systems, this paper investigates the question of which topological properties can be thus expressed. We introduce a novel, two-tiered logic for expressing topological properties, called CL, which is subsumed by first-order logic over the reals. We put forward the question whether the two logics are actually equivalent (when restricting attention to topological properties). We answer this question affirmatively on the class of “region databases”. We also prove a general result which further illustrates the power of the logic CL.