Abstract
The description logic \(\mathcal{SHI}\) extends the basic description logic \(\mathcal{ALC}\) with transitive roles, role hierarchies and inverse roles. The known tableau-based decision procedure [9] for \(\mathcal{SHI}\) exhibit (at least) NEXPTIME behaviour even though \(\mathcal{SHI}\) is known to be EXPTIME-complete. The automata-based algorithms for \(\mathcal{SHI}\) often yield optimal worst-case complexity results, but do not behave well in practice since good optimisations for them have yet to be found. We extend our method for global caching in \(\mathcal{ALC}\) to \(\mathcal{SHI}\) by adding analytic cut rules, thereby giving the first EXPTIME tableau-based decision procedure for \(\mathcal{SHI}\), and showing one way to incorporate global caching and inverse roles.
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