Determinacy of Real Conjunctive Queries. The Boolean Case

In their classical 1993 paper Chaudhuri and Vardi notice that some fundamental database theory results and techniques fail to survive when we try to see query answers as bags (multisets) of tuples rather than as sets of tuples. But disappointingly, almost 30 years later the bag-semantics based database theory is still in the infancy. We do not even know whether conjunctive query containment is decidable. And this is not due to lack of interest, but because, in the multiset world, everything suddenly gets discouragingly complicated. In this paper we try to re-examine, in the bag semantics scenario, the query determinacy problem, which has recently been intensively studied in the set semantics scenario. We show that query determinacy (under bag semantics) is decidable for boolean conjunctive queries and undecidable for unions of such queries (in contrast to the set semantics scenario, where the UCQ case remains decidable even for unary queries). We also show that -- surprisingly -- for path queries determinacy under bag semantics coincides with determinacy under set semantics (and thus it is decidable).