We study in this paper provenance information for queries with aggregation.
Provenance information was studied in the context of various query languages
that do not allow for aggregation, and recent work has suggested to capture
provenance by annotating the different database tuples with elements of a
commutative semiring and propagating the annotations through query evaluation.
We show that aggregate queries pose novel challenges rendering this approach
inapplicable. Consequently, we propose a new approach, where we annotate with
provenance information not just tuples but also the individual values within
tuples, using provenance to describe the values computation. We realize this
approach in a concrete construction, first for "simple" queries where the
aggregation operator is the last one applied, and then for arbitrary (positive)
relational algebra queries with aggregation; the latter queries are shown to be
more challenging in this context. Finally, we use aggregation to encode queries
with difference, and study the semantics obtained for such queries on
provenance annotated databases
