Tree-like Queries in OWL 2 QL: Succinctness and Complexity Results

TL;DR

This paper explores how the shape of conjunctive queries affects their answerability and rewriting size in OWL 2 QL ontologies, revealing both limitations and efficient cases for query rewriting and answering.

Contribution

It provides new bounds on the size of query rewritings and analyzes the complexity of query answering for various query classes in OWL 2 QL.

Findings

Superpolynomial lower bounds for PE-rewritings of linear queries.

Existence of polynomial-size NDL-rewritings for certain tree-shaped queries.

Tractability results for query answering in specific query-ontology configurations.

Abstract

This paper investigates the impact of query topology on the difficulty of answering conjunctive queries in the presence of OWL 2 QL ontologies. Our first contribution is to clarify the worst-case size of positive existential (PE), non-recursive Datalog (NDL), and first-order (FO) rewritings for various classes of tree-like conjunctive queries, ranging from linear queries to bounded treewidth queries. Perhaps our most surprising result is a superpolynomial lower bound on the size of PE-rewritings that holds already for linear queries and ontologies of depth 2. More positively, we show that polynomial-size NDL-rewritings always exist for tree-shaped queries with a bounded number of leaves (and arbitrary ontologies), and for bounded treewidth queries paired with bounded depth ontologies. For FO-rewritings, we equate the existence of polysize rewritings with well-known problems in Boolean circuit complexity. As our second contribution, we analyze the computational complexity of query answering and establish tractability results (either NL- or LOGCFL-completeness) for a range of query-ontology pairs. Combining our new results with those from the literature yields a complete picture of the succinctness and complexity landscapes for the considered classes of queries and ontologies.