An Algebraic View on p-Admissible Concrete Domains for Lightweight Description Logics

Concrete domains have been introduced in Description Logics (DLs) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. To retain decidability when integrating a concrete domain into a decidable DL, the domain must satisfy quite strong restrictions. In previous work, we have analyzed the most prominent such condition, called \(\omega \)-admissibility, from an algebraic point of view. This provided us with useful algebraic tools for proving \(\omega \)-admissibility, which allowed us to find new examples for concrete domains whose integration leaves the prototypical expressive DL \(\mathcal {ALC}\) decidable.