Conjunctive Query Answering for the Description Logic SHIQ

TL;DR

This paper investigates conjunctive query answering in the Description Logic SHIQ, allowing transitive roles in queries and knowledge bases, establishing decidability and tight complexity bounds for this problem.

Contribution

It introduces a decidable framework for conjunctive query answering in SHIQ with transitive roles, providing optimal complexity bounds.

Findings

Decidability of query answering with transitive roles in SHIQ

Deterministic algorithm with single exponential time in KB size

Double exponential time complexity in query size, optimal

Abstract

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.