TABLEAUX 2007: Automated Reasoning with Analytic Tableaux and Related Methods pp 133-148 | Cite as
EXPTIME Tableaux with Global Caching for Description Logics with Transitive Roles, Inverse Roles and Role Hierarchies
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.
Keywords
Static Rule Decision Procedure Description Logic Status Unsat Atomic ConceptPreview
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References
- 1.Baader, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69, 5–40 (2001)MATHCrossRefMathSciNetGoogle Scholar
- 2.De Giacomo, G., Massacci, F.: Combining deduction and model checking into tableaux and algorithms for Converse-PDL. Information and Computation, pp. 117–137, pp. 87–138 (2000)Google Scholar
- 3.Ding, Y., Haarslev, V.: Tableau caching for description logics with inverse and transitive roles. In: Proc. DL-2006: International Workshop on Description Logics, pp. 143–149 (2006)Google Scholar
- 4.Donini, F., Massacci, F., EXPTIME,: tableaux for ALC. Artificial Intelligence 124, 87–138 (2000)MATHCrossRefMathSciNetGoogle Scholar
- 5.Goré, R.: Tableau methods for modal and temporal logics. In: Agostino, D. (ed.) Handbook of Tableau Methods, pp. 297–396. Kluwer, Dordrecht (1999)Google Scholar
- 6.Goré, R., Nguyen, L.A.: Optimised EXPTIME tableaux for ALC using sound global caching, propagation and cutoffs. Manuscript (2007)Google Scholar
- 7.Heuerding, A., Seyfried, M., Zimmermann, H.: Efficient loop-check for backward proof search in some non-classical logics. In: Miglioli, P., Moscato, U., Ornaghi, M., Mundici, D. (eds.) TABLEAUX 1996. LNCS, vol. 1071, pp. 210–225. Springer, Heidelberg (1996)Google Scholar
- 8.Horrocks, I., Patel-Schneider, P.F.: Optimizing description logic subsumption. Journal of Logic and Computation 9(3), 267–293 (1999)MATHCrossRefMathSciNetGoogle Scholar
- 9.Horrocks, I., Sattler, U.: A description logic with transitive and inverse roles and role hierarchies. J. Log. Comput. 9(3), 385–410 (1999)MATHCrossRefMathSciNetGoogle Scholar
- 10.Nguyen, L.A.: Analytic tableau systems and interpolation for the modal logics KB, KDB, K5, KD5. Studia Logica 69(1), 41–57 (2001)MATHCrossRefMathSciNetGoogle Scholar
- 11.Rautenberg, W.: Modal tableau calculi and interpolation. JPL 12, 403–423 (1983)MATHCrossRefMathSciNetGoogle Scholar