Ontology-Mediated Queries: Combined Complexity and Succinctness of Rewritings via Circuit Complexity
This work addresses fundamental computational challenges in ontology-based data access for database and semantic web researchers, providing incremental theoretical insights.
The paper tackles the computational problems of succinctness and complexity for ontology-mediated queries in OWL 2 QL, classifying queries by shape and ontology depth to determine combined complexity and polynomial-size rewritings, with results based on a new hypergraph program model.
We give solutions to two fundamental computational problems in ontology-based data access with the W3C standard ontology language OWL 2 QL: the succinctness problem for first-order rewritings of ontology-mediated queries (OMQs), and the complexity problem for OMQ answering. We classify OMQs according to the shape of their conjunctive queries (treewidth, the number of leaves) and the existential depth of their ontologies. For each of these classes, we determine the combined complexity of OMQ answering, and whether all OMQs in the class have polynomial-size first-order, positive existential, and nonrecursive datalog rewritings. We obtain the succinctness results using hypergraph programs, a new computational model for Boolean functions, which makes it possible to connect the size of OMQ rewritings and circuit complexity.