  We present a consequence-based calculus for concept subsumption and
classification in the description logic ALCHOIQ, which extends ALC with role
hierarchies, inverse roles, number restrictions, and nominals. By using
standard transformations, our calculus extends to SROIQ, which covers all of
OWL 2 DL except for datatypes. A key feature of our calculus is its
pay-as-you-go behaviour: unlike existing algorithms, our calculus is worst-case
optimal for all the well-known proper fragments of ALCHOIQ, albeit not for the
full logic.
