Safe Database Queries with Arithmetic Relations

We consider the theory of database queries on a relational data model that includes a set of fixed relations used to model arithmetic comparisons and operations. We describe how to extend several natural query languages such as first-order logic, Datalog, and stratified Datalog to apply to databases in this model, and show that their relative expressive power is the same as it is for the standard relational model. We also show how properties such as domain independence and finiteness can be defined for queries in this data model, and show how the relationship between these properties varies from that in the standard model. As these properties are undecidable in general, we introduce a natural syntactic class of safe queries, that includes previous such classes, and study the extent to which it implies domain independence and finiteness. Finally, we give a simple procedure for translating safe first-order queries into relational algebra expressions as a basis for evaluating safe queries..