Finitely representable databases (extended abstract)

This work investigates the theory of finitely representable models and proves that it differs strongly from both classical model theory and finite model theory, and shows that most of the well known theorems of either one fail.

Abstract

We study classes of infinite but finitely representable databases based on constraints, motivated by new database applications such as geographical databases. The mathematical framework is based on classical decidable first-order theories. We investigate the theory of finitely representable models and prove that it differs strongly from both classical model theory and finite model theory. In particular, we show that most of the well known theorems of either one fail (compactness, completeness, locality, 0/1 laws, etc.). An immediate consequence is the lack of tools to consider the definability of queries in the relational calculus over finitely representable databases. We illustrate this very challenging problem through some classical examples.