Local properties of query languages

Abstract

Expressiveness of database query languages remains the major motivation for research in finite model theory. However, most techniques in finite model theory are based on Ehrenfeucht-Fraisse games, whose application often involves a rather intricate argument. Furthermore, most tools apply to first-order logic and some of its extensions, but not to languages that resemble real query languages, like SQL.

In this paper we use locality to analyze expressiveness of query languages. A query is local if, to determine if a tuple belongs to the output, one only has to look at a certain predetermined portion of the input.

We study local properties of queries in a context that goes beyond the pure first-order case, and then apply the resulting tools to analyze expressive power of SQL-like languages. We first prove a general result describing outputs of local queries, that leads to many easy inexpressibility proofs. We then consider a closely related bounded degree property, which describes the outputs of queries on structures that locally look “simple,” and makes inexpressibility proofs particularly easy. We prove that every local query has this property. Since every relational calculus (first-order) query is local, these results can be viewed as “off-the-shelf” strategies for inexpressibility proofs, which are often easier to apply than the games. We also show that some generalizations of the bounded degree property that were conjectured to hold, fail for relational calculus.

We then prove that the language obtained from relational calculus by adding grouping and aggregates (essentially plain SQL), has the bounded degree property, thus solving an open problem. Consequently, first-order queries with Härtig and Rescher quantifiers have the bounded degree property. Finally, we apply our results to show that SQL and relational calculus are incapable of maintaining the transitive closure view even in the presence of certain kinds of auxiliary data.