Equivalence of Keyed Relational Schemas by Conjunctive Queries

The concept of two schemas being equivalent is fundamental to database design, schema integration, and data model translation. An important notion of schema equivalence, query equivalence, was introduced by Atzeni et al., and used to evaluate the correctness of schema transformations. The logically equivalent notion of calculous equivalence, as well as three progressively more general notions of schema equivalence were introduced in 1984 by Hull, who showed that two schemas with no dependencies are equivalent (under all four notions of equivalence) if and only if they are identical (up to renaming and re-ordering of attributes and relations). Hull also conjectured that the same result holds for schemas with primary keys. In this work, we resolve the conjecture in the affirmative for the case of query equivalence based on mappings using conjunctive relational queries with equality selections.