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Global Caching for Coalgebraic Description Logics

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Automated Reasoning (IJCAR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6173))

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Abstract

Coalgebraic description logics offer a common semantic umbrella for extensions of description logics with reasoning principles outside relational semantics, e.g. quantitative uncertainty, non-monotonic conditionals, or coalitional power. Specifically, we work in coalgebraic logic with global assumptions (i.e. a general TBox), nominals, and satisfaction operators, and prove soundness and completeness of an associated tableau algorithm of optimal complexity ExpTime. The algorithm uses the (known) tableau rules for the underlying modal logics, and is based on on global caching, which raises hopes of practically feasible implementation. Instantiation of this result to concrete logics yields new algorithms in all cases including standard relational hybrid logic.

The second and third author supported by EPSRC grant EP/F031173/1. The last author supported by BMBF grant FormalSafe (FKZ 01IW07002).

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References

  1. Areces, C., ten Cate, B.: Hybrid logics. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic. Elsevier, Amsterdam (2007)

    Google Scholar 

  2. Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  3. Bolander, T., Blackburn, P.: Termination for hybrid tableaus. J. Log. Comput. 17, 517–554 (2007)

    Article  MathSciNet  Google Scholar 

  4. Bolander, T., Braüner, T.: Tableau-based decision procedures for hybrid logic. J. Log. Comput. 16(6), 737–763 (2006)

    Article  MathSciNet  Google Scholar 

  5. Calin, G., Myers, R., Pattinson, D., Schröder, L.: CoLoSS: The coalgebraic logic satisfiability solver (system description). In: Methods for Modalities, M4M-5. ENTCS. Elsevier, Amsterdam (to appear, 2008)

    Google Scholar 

  6. Cîrstea, C., Kupke, C., Pattinson, D.: EXPTIME tableaux for the coalgebraic μ-calculus. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 179–193. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. D’Agostino, G., Visser, A.: Finality regained: A coalgebraic study of Scott-sets and multisets. Arch. Math. Logic 41, 267–298 (2002)

    Article  MathSciNet  Google Scholar 

  8. Donini, F.M., Massacci, F.: EXPTIME tableaux for ALC. Artif. Intell. 124, 87–138 (2000)

    Article  Google Scholar 

  9. Gore, R., Kupke, C., Pattinson, D.: Optimal tableau algorithms for coalgebraic logics. In: Tools and Algorithms for the Construction and Analysis of Systems, TACAS 10. LNCS. Springer, Heidelberg (2010)

    MATH  Google Scholar 

  10. Goré, R., Nguyen, L.: EXPTIME tableaux for \(\mathcal{ALC}\) using sound global caching. In: Description Logics, DL ’07, CEUR Workshop Proceedings, vol. 250 (2007)

    Google Scholar 

  11. Goré, R., Nguyen, L.: EXPTIME tableaux with global caching for description logics with transitive roles, inverse roles and role hierarchies. In: Olivetti, N. (ed.) TABLEAUX 2007. LNCS (LNAI), vol. 4548, pp. 133–148. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Horrocks, I., Patel-Schneider, P.F.: Optimising description logic subsumption. J. Logic Comput. 9, 267–293 (1999)

    Article  MathSciNet  Google Scholar 

  13. Larsen, K., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94, 1–28 (1991)

    Article  MathSciNet  Google Scholar 

  14. Myers, R., Pattinson, D., Schröder, L.: Coalgebraic hybrid logic. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 137–151. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  15. Pattinson, D.: Coalgebraic modal logic: Soundness, completeness and decidability of local consequence. Theoret. Comput. Sci. 309, 177–193 (2003)

    Article  MathSciNet  Google Scholar 

  16. Pattinson, D., Schröder, L.: Cut elimination in coalgebraic logics. Inf. Comput. (to appear)

    Google Scholar 

  17. Schröder, L.: A finite model construction for coalgebraic modal logic. J. Log. Algebr. Prog. 73, 97–110 (2007)

    Article  MathSciNet  Google Scholar 

  18. Schröder, L., Pattinson, D.: Modular algorithms for heterogeneous modal logics. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 459–471. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  19. Schröder, L., Pattinson, D.: PSPACE bounds for rank-1 modal logics. ACM Trans. Comput. Log. 10, 13:1–13:33 (2009); Earlier version in LICS’06 (2006)

    Article  MathSciNet  Google Scholar 

  20. Schröder, L., Pattinson, D., Kupke, C.: Nominals for everyone. In: International Joint Conferences on Artificial Intelligence, IJCAI 09, pp. 917–922. AAAI Press, Menlo Park (2009)

    Google Scholar 

  21. Thomas, W.: On the synthesis of strategies in infinite games. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 1–13. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Laboratory, The Australian National University, Australia

    Rajeev Goré

  2. Department of Computing, Imperial College London, UK

    Clemens Kupke & Dirk Pattinson

  3. DFKI Bremen and Department of Computer Science, Universität Bremen, Germany

    Lutz Schröder

Authors
  1. Rajeev Goré
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  2. Clemens Kupke
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  3. Dirk Pattinson
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  4. Lutz Schröder
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Editor information

Editors and Affiliations

  1. RWTH Aachen, LuFG Informatik, 2, Ahornstr. 55, 52074, Aachen, Germany

    Jürgen Giesl

  2. Department of Computer Science, Chalmers University of Technology, 41296, Gothenburg, Sweden

    Reiner Hähnle

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Goré, R., Kupke, C., Pattinson, D., Schröder, L. (2010). Global Caching for Coalgebraic Description Logics. In: Giesl, J., Hähnle, R. (eds) Automated Reasoning. IJCAR 2010. Lecture Notes in Computer Science(), vol 6173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14203-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-14203-1_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14202-4

  • Online ISBN: 978-3-642-14203-1

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