Foundations of aggregation constraints

Abstract

We introduce a new constraint domain, aggregation constraints, that is useful in database query languages, and in constraint logic programming languages that incorporate aggregate functions. We formally study the fundamental problem of determining if a conjunction of aggregation constraints is satisfiable, and show that, for many classes of aggregation constraints, the problem is undecidable. We describe a complete and minimal axiomatization of aggregation constraints, for the SQL aggregate functions min, max, sum, count and average, over a non-empty, finite multiset on several domains. This axiomatization helps identify classes of aggregation constraints for which the satisfiability check i..