[Paper Review] Theoretically Optimal Datalog Rewritings for OWL 2 QL Ontology-Mediated Queries

Meghyn Bienvenu, Stanislav Kikot+3 more|arXiv (Cornell University)|Apr 18, 2016

Semantic Web and Ontologies20 references3 citations

TL;DR

This paper presents theoretically optimal nonrecursive Datalog rewritings for OWL 2 QL ontology-mediated queries (OMQs) in three key classes: bounded-depth ontologies with bounded-treewidth CQs, bounded-depth ontologies with bounded-leaf tree-shaped CQs, and arbitrary ontologies with bounded-leaf tree-shaped CQs. It shows that these rewritings can be constructed and evaluated in optimal combined complexity classes—LOGCFL, NL, and LOGCFL, respectively—matching the inherent complexity of OMQ evaluation.

ABSTRACT

We show that, for OWL 2 QL ontology-mediated queries with (i) ontologies of bounded depth and conjunctive queries of bounded treewidth, (ii) ontologies of bounded depth and bounded-leaf tree-shaped conjunctive queries, and (iii) arbitrary ontologies and bounded-leaf tree-shaped conjunctive queries, one can construct and evaluate nonrecursive datalog rewritings by, respectively, LOGCFL, NL and LOGCFL algorithms, which matches the optimal combined complexity.

Motivation & Objective

• To close the gap between the theoretical complexity of OWL 2 QL ontology-mediated query (OMQ) evaluation and the practicality of query rewriting techniques.
• To demonstrate that nonrecursive Datalog (NDL) rewritings for specific classes of OMQs can be constructed and evaluated in complexity classes matching the optimal combined complexity of OMQ evaluation.
• To provide a theoretically optimal rewriting framework that ensures space efficiency and high parallelizability for OMQs with structured CQs and bounded ontology depth.
• To validate the practical feasibility of these optimal rewritings by comparing them with existing systems like Clipper and Rapid on synthetic datasets.

Proposed method

• Constructs nonrecursive Datalog rewritings for three classes of OWL 2 QL OMQs using complexity-theoretic arguments grounded in circuit complexity and logic.
• Employs a normalization technique to transform TBoxes into normal form, ensuring that existential quantifiers are represented via concept names, simplifying reasoning.
• Applies structural decompositions—treewidth for general CQs and bounded-leaf tree-shape for specialized CQs—to control the complexity of rewritings.
• Uses the complexity classes LOGCFL and NL as upper bounds for the construction and evaluation of rewritings, matching the known combined complexity of OMQ evaluation.
• Employs a formal framework to prove that the size of the rewritings remains polynomial in the input size under the specified constraints.
• Validates the approach via empirical evaluation on Erdős–Rényi random graphs with varying parameters, using RDFox triplestore to measure evaluation time and output size.

Experimental results

Research questions

• RQ1 Can nonrecursive Datalog rewritings be constructed for OWL 2 QL OMQs with bounded ontology depth and bounded-treewidth CQs in LOGCFL time?
• RQ2 Is it possible to achieve optimal complexity for OMQs with bounded-depth ontologies and bounded-leaf tree-shaped CQs using NDL rewritings in NL?
• RQ3 Can optimal NDL rewritings be constructed for arbitrary ontologies when the CQs are bounded-leaf tree-shaped, achieving LOGCFL complexity?
• RQ4 Do the theoretically optimal rewritings outperform or match the performance of existing query rewriting engines like Clipper and Rapid in practice?

Key findings

• For OMQs with bounded-depth ontologies and bounded-treewidth CQs, the paper constructs NDL rewritings that can be evaluated in LOGCFL, matching the optimal combined complexity.
• For OMQs with bounded-depth ontologies and bounded-leaf tree-shaped CQs, the construction and evaluation of NDL rewritings are achievable in NL, which is optimal.
• For OMQs with arbitrary ontologies and bounded-leaf tree-shaped CQs, the method achieves LOGCFL complexity, matching the known optimal combined complexity.
• Empirical evaluation on synthetic datasets shows that the proposed optimal rewritings produce results consistent with Clipper and Rapid, with competitive evaluation times and correct output sizes.
• The optimal rewritings avoid super-polynomial blowup in size, unlike positive existential (PE) rewritings, which can be too large for polynomial-time evaluation.
• The results confirm that the theoretical complexity bounds are not only tight but also practically realizable, as demonstrated by the evaluation on datasets with up to 20,000 vertices and varying edge and concept probabilities.