CWA-solutions for data exchange settings with target dependencies

TLDR: The present paper extends Libkin's notion of CWA-solutions to data exchange settings with target dependencies, and it is obtained that also the EXISTENCE-OF-UNIVERSAL-SOLUTIONS problem is undecidable in genera.

Abstract: Data exchange deals with the following problem: given an instance over a source schema, a specification of the relationship between the source and the target,and dependencies on the target, construct an instance over a target schema that satisfies the given relationships and dependencies. Recently - for data exchange settings without target dependencies - Libkin (PODS'06) introduced a new concept of solutions based on the closed world assumption (so calledCWA-solutions), and showed that, in some respects, this new notion behaves better than the standard notion of solutions considered in previous papers on data exchange. The present paper extends Libkin's notion of CWA-solutions to data exchange settings with target dependencies. We show that, when restricting attention to data exchange settings with weakly acyclic target dependencies, this new notion behaves similarly as before: the core is the unique "minimal" CWA-solution, and computing CWA-solutions as well as certain answers to positive queries is possible in polynomial time and can be PTIME-hard. However, there may be more than one "maximal" CWA-solution. And going beyond the class of positive queries, we obtain that there are conjunctive queries with (just) one inequality, for which evaluating the certain answers is coNP-hard. Finally, we consider the EXISTENCE-OF-CWA-SOLUTIONS problem: while the problem is tractable for data exchange settings with weakly acyclic target dependencies, it turns out to be undecidable for general data exchange settings. As a consequence, we obtain that also the EXISTENCE-OF-UNIVERSAL-SOLUTIONS problem is undecidable in genera.