On First-Order Topological Queries

International audienceOne important class of spatial database queries is the class of topological queries, that is, queries invariant under homeomorphisms. We study topological queries expressible in the standard query language on spatial databases, rst-order logic with various amounts of arithmetic. Our main technical result is a combinato-rial characterization of the expressive power of topological rst-order logic on regular spatial databases

Finitely Representable Databases

We study infinite but finitely representable databases based on constraints, motivated by new database applications such as those involving spatio-temporal information. We introduce a general definition of finite representation, and define the concept of a query as a generalization of a query over relational databases. We investigate the theory of finitely representable models and prove that it differs from both classical model theory and finite model theory. In particular, we show the failure of most of the well known theorems of logic (compactness, completeness, etc.). An important consequence is that properties such as query satisfiability and containment are undecidable. We illustrate the use of Ehrenfeucht-Frasse games on the expressive power of query languages over finitely representable databases. As a case study, we focus on queries over dense order constraint databases. We consider in particular "order-generic" queries which are mappings closed under order-preserving bijection..