[Paper Review] First Order-Rewritability and Containment of Conjunctive Queries in Horn Description Logics

Meghyn Bienvenu, Peter Hansen+2 more|arXiv (Cornell University)|Nov 19, 2020

Semantic Web and Ontologies24 references42 citations

TL;DR

This paper analyzes FO-rewritability and containment of conjunctive queries under ontologies in Horn description logics between EL and Horn-SHIF, providing complexity results and automata-based decision procedures.

ABSTRACT

We study FO-rewritability of conjunctive queries in the presence of ontologies formulated in a description logic between EL and Horn-SHIF, along with related query containment problems. Apart from providing characterizations, we establish complexity results ranging from ExpTime via NExpTime to 2ExpTime, pointing out several interesting effects. In particular, FO-rewriting is more complex for conjunctive queries than for atomic queries when inverse roles are present, but not otherwise.

Motivation & Objective

• Motivate efficient query answering under ontologies by studying FO-rewritability for CQs in Horn DLs between EL and Horn-SHIF.
• Characterize when FO-rewritings exist for OMQs with CQ queries and identify how inverse roles affect complexity.
• Link FO-rewritability with query containment, and establish connections to automata-theoretic decision procedures.

Proposed method

• Provide semantic characterizations of FO-rewritability using (pseudo) tree-shaped ABoxes and unwindings.
• Prove complexity results (ExpTime, 2ExpTime, coNExpTime) for FO-rewritability and containment across OMQ languages.
• Reduce Horn-SHIF cases to EL-IHFbot cases via normal-form TBoxes and polynomial-time transformations.
• Develop automata-based decision procedures using two-way alternating parity automata to handle pseudo tree ABoxes.
• Leverage Ehrenfeucht-Fraïssé style locality arguments and pumping techniques to bound the necessary ABox sizes for FO-rewritability decisions.

Experimental results

Research questions

• RQ1 For which ontology-mediated query languages (between EL, ELIF, and Horn-SHIF) is FO-rewritability of conjunctive queries decidable?
• RQ2 What are the exact complexity bounds for FO-rewritability and containment when using CQs under these DL ontologies, and how do inverse roles influence them?
• RQ3 Can FO-rewritability be effectively reduced to containment or to FO-rewritability of rooted/conjoined CQ fragments?
• RQ4 How can automata-theoretic approaches be used to decide FO-rewritability and containment, and what are the resulting state complexities?
• RQ5 Does restricting to rooted CQs or to ABoxes without inverses alter the complexity landscape significantly?

Key findings

• FO-rewritability and containment are 2ExpTime-complete for languages from (ELI) to (Horn-SHIF) with CQ queries.
• FO-rewritability and containment are ExpTime-complete for languages from (EL) to (ELHF_bot) with CQ queries.
• Inverse roles increase complexity for CQ queries but not for atomic queries.
• When restricting to rooted CQs, the complexity drops to coNExpTime for the same language classes.
• There is a close relationship between FO-rewritability, containment, and ABox inconsistency, with polynomial-time reductions guiding the analysis.
• If an OMQ from (Horn-SHIF, CQ) is FO-rewritable, a UCQ-rewriting can be effectively constructed.