On higher-order description logics

We investigate an extension of Description Logics 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, and full metamodeling, providing the ability of using the language constructors and operators as predicate arguments, in the style of RDF. We argue that higher-order features of the former 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 reasoning in DLs extended with such features. In particular, we show that adding domain metamodeling capabilities to expressive DLs has no impact on the complexity of the various reasoning tasks