Theory of Database Queries with Arithmetic Relations

We consider the theory of database queries on a relational data model that includes a set of xed relations used to model arithmetic comparisons and operations. We describe how to extend several natural query languages such as rst-order logic, Datalog, and strati ed Datalog to 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. The addition of aggregate operations extends the relative expressive power of each of the above languages independently of the extension to the next most expressive language. We also show how properties such as domain independence and niteness can be de ned 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 niteness. Finally, we give a simple procedure for translating safe rstorder queries into relational algebra expressions as a basis for evaluating safe queries in all of the above query classes.