Data Complexity in Expressive Description Logics With Path Expressions

TL;DR

This paper analyzes the data complexity of the satisfiability problem in a highly expressive description logic, ZOIQ, establishing NP-completeness over quasi-forests and coNEXPTIME-completeness for entailment of rooted queries, thus completing the complexity landscape.

Contribution

It provides a comprehensive complexity analysis of ZOIQ's satisfiability and entailment problems, extending understanding of decidable fragments and their computational bounds.

Findings

Satisfiability in ZOIQ is NP-complete over quasi-forests.

Entailment of rooted queries in ZIQ is coNEXPTIME-complete.

Completes the data complexity landscape for decidable ZOIQ fragments.

Abstract

We investigate the data complexity of the satisfiability problem for the very expressive description logic ZOIQ (a.k.a. ALCHb Self reg OIQ) over quasi-forests and establish its NP-completeness. This completes the data complexity landscape for decidable fragments of ZOIQ, and reproves known results on decidable fragments of OWL2 (SR family). Using the same technique, we establish coNEXPTIME-completeness (w.r.t. the combined complexity) of the entailment problem of rooted queries in ZIQ.