Relational completeness of query languages for annotated databases

Annotated relational databases can be queried either by simply making the annotations explicitly available along the ordinary data, or by adapting the standard query operators so that they have an implicit effect also on the annotations. We compare the expressive power of these two approaches. As a formal model for the implicit approach we propose the color algebra, an adaptation of the relational algebra to deal with the annotations. We show that the color algebra is relationally complete: it is equivalent to the relational algebra on the explicit annotations. Our result extends a similar completeness result established for the query algebra of the MONDRIAN annotation system, from unions of conjunctive queries to the full relational algebra. We also show that the color algebra is nonredundant: no operator can be expressed in terms of the other operators. We also present a generalization of the color algebra that is relationally complete in the presence of built-in predicates on the annotations.