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

  • Rajeev Goré
  • Linh Anh Nguyen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4548)


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.


Static Rule Decision Procedure Description Logic Status Unsat Atomic Concept 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Rajeev Goré
    • 1
  • Linh Anh Nguyen
    • 2
  1. 1.The Australian National University and NICTA, Canberra ACT 0200Australia
  2. 2.Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097 WarsawPoland

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