Krötzsch

Nominal schemas extend description logics (DLs) with a restricted form of variables, thus integrating rule-like expressive power into standard DLs. They are also one of the most recently introduced DL features, and in spite of many works on algorithms and implementations, almost nothing is known about their computational complexity and expressivity. We close this gap by providing a comprehensive analysis of the reasoning complexities of a wide range of DLs--from EL to SROIQ--extended with nominal schemas. Both combinedand data complexities increase by one exponential in most cases, with the one previously known case of SROIQ being the main exception. Our proofs employ general modeling techniques that exploit the power of nominal schemas to succinctly represent many axioms, and which can also be applied to study DLs beyond those we consider.