An Extended Algebra for Constraint

| Constraint relational databases use constraints to both model and query data. A constraint relation contains a nite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the speciic conjunction of constraints, it may possibly represent an in-nite set of relational tuples. For their characteristics, constraint databases are well suited to model multidimensional and structured data, like spatial and temporal data. The deenition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology. In this paper, we extend the previously deened constraint algebra (called generalized relational algebra). First, we show that the relational model is not the only possible semantic reference model for constraint relational databases and we show how constraint relations can be interpreted under the nested relational model. Then, we introduce two distinct classes of constraint algebras, one based on the re-lational algebra, and one based on the nested relational algebra , and we present an algebra of the latter type. The algebra is proved equivalent to the generalized relational algebra when input relations are modiied by introducing generalized tuple identiiers. However, it is more suitable from a user point of view. Thus, the diierence existing between such algebras is similar to the diierence existing between the relational algebra and the nested relational algebra, dealing with only one level of nesting. We also show how external functions can be added to the proposed algebra.