First-order definability over constraint databases

Abstract

In this paper, we study the expressive power of first-order logic as a query language over constraint databases. We consider constraints over various domains (ℕ,2e, ℝ), and with various operations (⩽, +, ×, x y). We first tackle the problem of the definability of parity and connectivity, which are the most classical examples of queries not expressible in first-order logic over finite structures. We prove that these two queries are first-order expressible in presence of (enough) arithmetic. This is in sharp contrast with classical relational databases. Nevertheless, we show that they are not definable with constraints of interest for constraint databases such as linear constraints. We then develop reductions techniques for queries over constraint databases, that allow us to draw conclusions with respect to their undefinability in various constraint query languages.KeywordsQuery LanguageRelation SymbolConnectivity QueryGraph QueryReal Closed FieldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.