Conservative Extensions in Horn Description Logics with Inverse Roles

TL;DR

This paper explores the decidability and complexity of conservative extensions in Horn description logics with inverse roles, providing decision procedures and complexity bounds for various DLs.

Contribution

It introduces a novel characterization combining unbounded and bounded homomorphisms, enabling decision procedures for conservative extensions with inverse roles.

Findings

Query conservative extensions are 2ExpTime-complete in specified DLs.

Deductive conservative extensions are 2ExpTime-complete in certain DLs.

Results hold for inseparability and entailment as well.

Abstract

We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative extensions, defined by requiring that the answers to all conjunctive queries are left unchanged, and deductive conservative extensions, which require that the entailed concept inclusions, role inclusions, and functionality assertions do not change. Upper bounds for query conservative extensions are particularly challenging because characterizations in terms of unbounded homomorphisms between universal models, which are the foundation of the standard approach to establishing decidability, fail in the presence of inverse roles. We resort to a characterization that carefully mixes unbounded and bounded homomorphisms and enables a decision procedure that combines tree automata and a mosaic technique. Our main results are that query conservative extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions are 2ExpTime-complete in all DLs between ELI and ELHIF_\bot. The same results hold for inseparability and entailment.