The Expressive Power of DL-Lite

TL;DR

This paper analyzes the expressive capabilities and computational properties of the description logic DL-Lite, revealing its limitations in expressing disjunction and its NP-complete query answering complexity.

Contribution

It characterizes the expressive power of DL-Lite using simulations and establishes its computational complexity for query answering.

Findings

Disjunction is not expressible in DL-Lite.

No simulation-based closure property exists for DL-Lite assertions.

Query answering for unions of conjunctive queries is NP-complete.

Abstract

Description logics are knowledge representation formalisms that provide the formal underpinning of the semantic web and in particular of the $\text{OWL}$ Ontology Web Language. In this paper we investigate the expressive power of logic $\text{DL-Lite}_{R,\sqcap}$, and some of its computational properties. We rely on simulations to characterize the absolute expressive power of $\text{DL-Lite}_{R,\sqcap}$ as a concept language, and to show that disjunction is not expressible. We also show that no simulation-based closure property exists for $\text{DL-Lite}_{R,\sqcap}$ assertions. Finally, we show that query answering of unions of conjunctive queries is $\text{NP-complete}$.