On the expressive power of database queries with intermediate types

The set-height of a complex object type is defined to be its level of nesting of the set construct. In a query of the complex object calculus which maps a database D to an output type T, an intermediate type is a type which is used by some variable of the query, but which is not present in D or T. For each k, i ≥ 0 we define CALCk,i to be the family of calculus queries mapping from and to types with set-height ≤ k and using intermediate types with set-height ≤ i In particular, CALC0,0 is the relational calculus, and CALC0,1 is equivalent to the family of second-order (relational) queriesSeveral results concerning these families of languages are obtained. A primary focus is on the families CALC0,i, which map relations to relations Upper bounds on the complexity of these families are provided, and it is shown that CALC0,3 has at least the complexity of exponential space. The CALC0,i hierarchy does not collapse, because for each i, CALC0,i is strictly less expressive than CALC0,i+2. The union ∪0≤iCALC0,i is strictly less expressive than the family of 'computable' database queries.The expressive power of queries from the complex object calculus interpreted using a semantics based on the use of arbitrarily large finite numbers of invented values is studied. Under this semantics, the expressive power of the relational calculus is not increased, and the CALC0,i hierarchy collapses at CALC0,1. We also consider queries which use a bounded number of invented values.