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

The description logic SHI extends the basic description logic ALC with transitive roles, role hierarchies and inverse roles. The known tableau-based decision procedure [9] for SHI exhibit (at least) NEXPTIME behaviour even though SHI is known to be EXPTIME-complete. The automata-based algorithms for 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 ALC to SHI by adding analytic cut rules, thereby giving the first EXPTIME tableau-based decision procedure for SHI, and showing one way to incorporate global caching and inverse roles.