Complete geometrical query languages

Abstract

We extend Chandra and Harel's seminal work on computable queries for relational databases to a setting in which also spatial data may be present, using a constraint-based data model. Concretely, we introduce both coordinate-based and point-based query languages that are complete in the sense that they can express precisely all computable queries that are generic with respect to certain classes of transformations of space, corresponding to certain geometric interpretations of spatial data. The languages we introduce are obtained by augmenting basic languages with a "while" construct. We also show that the respective basic point-based languages are complete, relative to the subclass of the corresponding generic queries consisting of those that are expressible in the relational calculus with real polynomial constraints.