The Complexity of Ontology-Based Data Access with OWL 2 QL and Bounded Treewidth Queries

Abstract

Our concern is the overhead of answering OWL 2 QL ontology-mediated queries (OMQs) in ontology-based data access compared to evaluating their underlying tree-shaped and bounded treewidth conjunctive queries (CQs). We show that OMQs with bounded-depth ontologies have nonrecursive datalog (NDL) rewritings that can be constructed and evaluated in LOGCFL for combined complexity, even in NL if their CQs are tree-shaped with a bounded number of leaves, and so incur no overhead in complexity-theoretic terms. For OMQs with arbitrary ontologies and bounded-leaf CQs, NDL-rewritings are constructed and evaluated in LOGCFL. We show experimentally feasibility and scalability of our rewritings compared to previously proposed NDL-rewritings. On the negative side, we prove that answering OMQs with treeshaped CQs is not fixed-parameter tractable if the ontology depth or the number of leaves in the CQs is regarded as the parameter, and that answering OMQs with a fixed ontology (of infinite depth) is NP-complete for tree-shaped and LOGCFL for bounded-leaf CQs.

Ontology-Mediated Queries

“…Consider the FO-formula Φ(x) obtained by replacing each p S (z ) in χ with S(z), each p t with tw t , and adding the appropriate prefix ∃y. By comparing (10) and (6), we see that Φ(x) is an FO-rewriting of Q(x) over complete data instances. This proves the following theorem for FO-and PE-rewritings; NDLrewritings are dealt with in Appendix A.2:…”

“…However, the LogCFL and NL membership results cannot be immediately inferred from the existence of polynomial-size NDL-rewritings, since evaluating polynomial-size NDL-queries is a PSpace-complete problem in general. In the follow-up paper [10], we give polynomial-size NDL-rewritings for these cases, which can be constructed and evaluated in LogCFL and NL, respectively, and study the parametrised and query complexities of OMQ answering with CQs of bounded treewidth.…”

When is Ontology-Mediated Querying Efficient?

“…Both the combined complexity and the data complexity of OMQ evaluation have received considerable interest in the literature, where data complexity means that the OMQ is fixed while the database is treated as an input, in line with the standard setup from database theory. The combined complexity ranges from PTIME [8], [9], [12] to at least 2EXPTIME [21], [31], [34]. Regarding the data complexity, there is an important divide between DLs that include negation or disjunction and induce CONP-hardness, and DLs that do not [16], [20], [27], [29].…”

STypeS: Nonrecursive Datalog Rewriter for Linear TGDs and Conjunctive Queries

“…It has been discovered [21,19], however, that the shortest FO-rewritings can be of superpolynomial size compared to the given CQ, which makes reduction (1) impractical. Further investigations [7][8][9] revealed that, by restricting the class of linear tgds to those of bounded arity and bounded existential depth and the class of CQs to those of bounded treewidth, one can achieve polynomial-size rewritings in the form of nonrecursive datalog (NDL) queries (rather than FO-formulas). In the context of Example 1, the following is a rewriting in the form of an NDL query with the goal predicate G:…”

“…(NDL queries can also be thought of as SQL queries with view definitions.) The NDLrewritings obtained in [8,9] are optimal in the sense that the combined complexity of constructing and evaluating them is the same (LOGCFL) as the complexity of evaluating the underlying CQs [29,15,20]. (Note that the shortest rewritings into positive existential formulas in this case can still be of superpolynomial size, while polynomial-size FO-rewritings exist iff LOGCFL/poly ⊆ NC 1 , which is highly doubtful.)…”