Probabilistic Ontological Data Exchange with Bayesian Networks

We study the problem of exchanging probabilistic data between ontology-based probabilistic databases. The probabilities of the probabilistic source databases are compactly encoded via Boolean formulas with the variables adhering to the dependencies imposed by a Bayesian network, which are closely related to the management of provenance. For the ontologies and the ontology mappings, we consider different kinds of existential rules from the Datalog+/– family. We provide a complete picture of the computational complexity of the problem of deciding whether there exists a probabilistic (universal) solution for a given probabilistic source database relative to a (probabilistic) ontological data exchange problem. We also analyze the complexity of answering UCQs (unions of conjunctive queries) in this framework.