Aggregation in Datalog Under Set Semantics

We propose an extension of Datalog that supports aggregates under set semantics and is as expressive as the previous extensions of Datalog which use bag semantics to represent aggregate programs. We show that under set semantics, our extension has greater expressive power than the previous extensions of Datalog which support aggregates. By expressing aggregate Datalog queries under set semantics, we can study the equivalence of the aggregate queries without defining notions of equivalence under set, bag-set and bag semantics separately. Under set semantics, Datalog programs with aggregation can be evaluated efficiently since the different derivations of goal tuples are not tracked. In our proposed extension, complex aggregation predicates can be built modularly using simple predicates. This modularity can be potentially leveraged to rewrite aggregate queries using aggregate views where the aggregation functions used in the query and the views are different.