Cheap Boolean Role Constructors for Description Logics

We investigate the possibility of incorporating Boolean role constructors on simple roles into some of today's most popular description logics, focussing on cases where those extensions do not increase complexity of reasoning. We show that the expressive DLs $\mathcal{SHOIQ}$ and $\mathcal{SROIQ}$, serving as the logical underpinning of OWL and the forthcoming OWL 2, can accommodate arbitrary Boolean expressions. The prominent OWL-fragment $\mathcal{SHIQ}$ can be safely extended by safe role expressions, and the tractable fragments $\mathcal{EL}^{++}$ and DLP retain tractability if extended by conjunction on roles, where in the case of DLP the restriction on role simplicity can even be discarded.

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