Linear Approximation of Planar Spatial Databases Using Transitive-Closure Logic

We consider spatial databases in the plane that can be defined by polynomial constraint formulas. Motivated by applications in geographic information systems, we investigate linear approximations of spatial databases and study in which language they can be expressed effectively. Specifically, we show that they cannot be expressed in the standard first-order query language for polynomial constraint databases but that an extension of this first-order language with transitive closure suces to express the approximation query in an effective manner. Furthermore, we introduce an extension of transitive-closure logic and show that this logic is complete for the computable queries on linear spatial databases. This result together with our first result implies that this extension of transitive-closure logic can express all computable topological queries on arbitrary spatial databases in the plane