We address the problem of handling provenance information in ELHr ontologies. We consider a setting recently introduced for ontology-based data access, based on semirings and extending classical data provenance, in which ontology axioms are annotated with provenance tokens. A consequence inherits the provenance of the axioms involved in deriving it, yielding a provenance polynomial as an annotation. We analyse the semantics for the ELHr case and show that the presence of conjunctions poses various difficulties for handling provenance, some of which are mitigated by assuming multiplicative idempotency of the semiring. Under this assumption, we study three problems: ontology completion with provenance, computing the set of relevant axioms for a consequence, and query answering.

We study the complexity of exchanging probabilistic data between ontology-based probabilistic databases. We consider the Datalog+/- family of languages as ontology and ontology mapping languages, and we assume different compact encodings of the probabilities of the probabilistic source databases via Boolean events. We provide an extensive complexity analysis of the problem of deciding the existence of a probabilistic (universal) solution for a given probabilistic source database relative to a (probabilistic) data exchange problem for the different languages considered.

We study the complexity of threshold query answering in the logical framework for probabilistic ontological data exchange, which is an extension of the classical probabilistic data exchange framework with (1) probabilistic databases compactly encoded with several different annotations according to three different probability models used and (2) existential rules of different expressiveness. The ontological data exchange framework provides a logical formalization of exchanging probabilistic data and knowledge from one ontology to another via either deterministic or probabilistic mappings. We define the threshold query answering task in this framework and provide a thorough analysis of its computational complexity for different classes of existential rules and types of complexity. We also delineate several classes of existential rules and a probability model along with a compact encoding in which the threshold query answering problem can be solved in polynomial time in the data complexity.

Abstract Recently, there has been a lot of interest in the integration of Description Logics (DL) and rules on the Semantic Web. We defineguarded hybrid knowledge bases(org-hybrid knowledge bases) as knowledge bases that consist of a Description Logic knowledge base and aguardedlogic program, similar to the $\mathcal{DL}$ +logknowledge bases from Rosati (In Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning, AAAI Press, Menlo Park, CA, 2006, pp. 68–78.). g-Hybrid knowledge bases enable an integration of Description Logics and Logic Programming where, unlike in other approaches, variables in the rules of a guarded program do not need to appear in positive non-DL atoms of the body, i.e., DL atoms can act asguardsas well. Decidability of satisfiability checking of g-hybrid knowledge bases is shown for the particular DL $\mathcal{DLRO}^{\-{le}}$ , which is close to OWL DL, by a reduction to guarded programs under the open answer set semantics. Moreover, we show 2-Exptime-completeness for satisfiability checking of such g-hybrid knowledge bases. Finally, we discuss advantages and disadvantages of our approach compared with $\mathcal{DL}$ +logknowledge bases.