Higher-order description logics for domain metamodeling

We investigate an extension of Description Logics (DL) with higher-order capabilities, based on Henkin-style semantics. Our study starts from the observation that the various possibilities of adding higher-order constructs to a DL form a spectrum of increasing expressive power, including domain metamodeling, i.e., using concepts and roles as predicate arguments. We argue that higher-order features of this type are sufficiently rich and powerful for the modeling requirements arising in many relevant situations, and therefore we carry out an investigation of the computational complexity of satisfiability and conjunctive query answering in DLs extended with such higher-order features. In particular, we show that adding domain metamodeling capabilities to script Sscript Hscript Iscript Q (the core of OWL 2) has no impact on the complexity of the various reasoning tasks. This is also true for DL-Litescript R (the core of OWL 2 QL) under suitable restrictions on the queries. Copyright © 2011, Association for the Advancement of Artificial Intelligence. All rights reserved.