Set-semantics versus bag-semantics testability

Determine whether the lower bounds established for bag semantics can be extended to set semantics, and whether there exist monadic Datalog queries that are constant query testable under set semantics but not under bag semantics.

Background

The paper’s lower-bound arguments for monadic Datalog property testing rely on bag databases, particularly on multiplicities used in reductions from hard conjunctive queries. The authors note that some technical structural results hold independently of higher multiplicities, but the property-testing lower bounds do not currently transfer to set semantics. They therefore ask whether the two semantics yield different testability behavior.