Existential Rules and Bayesian Networks for Probabilistic Ontological Data Exchange

We investigate the problem of exchanging probabilistic data between ontology-based probabilistic databases. The probabilities of the probabilistic source databases are compactly and flexibly encoded via Bayesian networks, which are closely related to the management of provenance. For the ontologies and the ontology mappings, we consider existential rules from the Datalog+/- family. We analyze 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 provide a host of complexity results for this problem for different classes of existential rules. We also analyze the complexity of answering UCQs (unions of conjunctive queries) in this framework.