Querying databases with knowledge domains

We assume that data domains are associated with a set of user-defined predicates, which we call knowledge domains and tackle the following problem: given a database equipped with knowledge domains, what exactly the set of relations can possibly be retrieved by a query? First, we extend the RA to the Knowledge Relational Algebra (the KRA) by allowing predicates to be used in formulae of the selection operator (σ). Based on the notion of powerdomain partition, which characterise a knowledge domain by partitioning on its finite powerset, we then exam the expressiveness of the KRA and show that it expresses exactly the set of all possible relations that are invariant under knowledge database automorphism of databases. We also develop the three lattices of: (1) knowledge domain classes, (2) query language classes and (3) computable queries, and show that these lattices are isomorphic to each other. Our result clarifies the implicit association between the three fundamental notions of databases