EXPTIME Tableaux with Global Caching for Description Logics with Transitive Roles, Inverse Roles and Role Hierarchies

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.