How expressive is stratified aggregation?

We present results on the expressive power of various deductive database languages extended with stratified aggregation. We show that (1) Datalog extended with stratified aggregation cannot express a query to count the number of paths between every pair of nodes in an acyclic graph, (2) Datalog extended with stratified aggregation and arithmetic on integers (the + operator) can express allcomputable queries on ordered domains, and (3) Datalog extended with stratified aggregation and generic function symbols can express allcomputable queries (on ordered or unordered domains). Note that without stratified aggregation, the above extensions of Datalog cannot express all computable queries. We show that replacing stratified aggregation by stratified negation preserves expressiveness. We identify subclasses of the above languages that are complete (can express all, and only the, computable queries).

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