|Abstrakt:||While there exist many description logics (DLs) with various expressivity, all of them are fragments of first-order logic. Thus, some domains with inherent higher-order structure cannot be straightforwardly modelled even in the most expressive standard DLs. Such standard DLs also lack the features that would allow to freely model with some of the language operators, e.g., the instantiation operator.
In this thesis, we propose four higher-order description logics with metamodelling features allowing to freely model with instantiation and partially also with subsumption. In addition, we show that our higher-order DLs have also other properties desirable for metamodelling. We prove their decidability by means of reduction to standard DLs. Further, we compare our higher-order DLs with other existing higher-order DLs.
Since the reduction is polynomial, our higher-order DLs can be decided by algorithms for standard DLs with the same complexity. Moreover, the reduction shows that the expressive power needed to model with higher orders to some extent is already present in the standard description logics.