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On the Complexity of Hybrid Logics with Binders

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Computer Science Logic (CSL 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3634))

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Abstract

Hybrid logic refers to a group of logics lying between modal and first-order logic in which one can refer to individual states of the Kripke structure. In particular, the hybrid logic HL(@, ↓ ) is an appealing extension of modal logic that allows one to refer to a state by means of the given names and to dynamically create new names for a state.

Unfortunately, as for the richer first-order logic, satisfiability for the hybrid logic HL(@, ↓ ) is undecidable and model checking for HL(@, ↓ ) is PSpace-complete. We carefully analyze these results and we isolate large fragments of HL(@, ↓ ) for which satisfiability is decidable and model checking is below PSpace.

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References

  1. Andréka, H., van Benthem, J., Németi, I.: Modal logics and bounded fragments of predicate logic. Journal of Philosophical Logic 27, 217–274 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Grädel, E.: On the restraining power of guards. Journal of Symbolic Logic 64, 1719–1742 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Mortimer, M.: On languages with two variables. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 21, 135–140 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  4. Grädel, E., Otto, M.: On logics with two variables. Theoretical computer science 224, 73–113 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Areces, C., Blackburn, P., Marx, M.: Hybrid logics: Characterization, interpolation, and complexity. Journal of Symbolic Logic 66, 977–1010 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. ten Cate, B.: Interpolation for extended modal languages. Journal of Symbolic Logic 70, 223–234 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. ten Cate, B.: Model theory for extended modal languages. PhD thesis, University of Amsterdam, ILLC Dissertation Series DS-2005-01 (2005)

    Google Scholar 

  8. Franceschet, M., de Rijke, M.: Model checking for hybrid logics (with an application to semistructured data). Journal of Applied Logics (2005) (to appear)

    Google Scholar 

  9. Blackburn, P., Seligman, J.: Hybrid languages. Journal of Logic, Language and Information 4, 251–272 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Harel, D.: Recurring dominoes: making the highly undecidable highly understandable. Annals of Discrete Mathematics 24, 51–72 (1985)

    MATH  MathSciNet  Google Scholar 

  11. Goranko, V.: Hierarchies of modal and temporal logics with reference pointers. Journal of Logic, Language, and Information 5, 1–24 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Areces, C., Blackburn, P., Marx, M.: A road-map on complexity for hybrid logics. In: Flum, J., Guez-Artalejo, M.R. (eds.) Proceedings of the 8th Annual Conference of the EACSL, Madrid (1999)

    Google Scholar 

  13. Marx, M.: Narcissists, stepmothers and spies. In: Proceedings of the International Workshop on Description Logics (2002)

    Google Scholar 

  14. Fisher, M., Ladner, R.: Propositional dynamic logic of regular programs. Journal of Computer and System Sciences 18, 194–211 (1979)

    Article  MathSciNet  Google Scholar 

  15. Areces, C., Blackburn, P., Marx, M.: The computational complexity of hybrid temporal logics. Logic Journal of the IGPL 8, 653–679 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  16. ten Cate, B., Franceschet, M.: Guarded fragments with constants. Journal of Logic, Language, and Information (2005) (to appear)

    Google Scholar 

  17. Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Springer, Berlin (1997)

    MATH  Google Scholar 

  18. ten Cate, B., Franceschet, M.: On the complexity of hybrid logics with binders. Technical Report PP-2005-02, ILLC, University of Amsterdam (2005)

    Google Scholar 

  19. Vardi, M.Y.: On the complexity of bounded-variable queries. In: Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 266–276 (1995)

    Google Scholar 

  20. ten Cate, B., Franceschet, M.: Guarded fragments with constants. Technical Report PP-2004-32, ILLC, University of Amsterdam (2004)

    Google Scholar 

  21. Blackburn, P.: Representation, reasoning, and relational structures: A hybrid logic manifesto. Logic Journal of the IGPL 8, 339–365 (2000)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Informatics Institute, University of Amsterdam, Kruislaan 403, 1098 SJ, Amsterdam, The Netherlands

    Balder ten Cate & Massimo Franceschet

  2. Department of Sciences, University “G. D’Annunzio”, Viale Pindaro, 42, 65127, Pescara, Italy

    Massimo Franceschet

Authors
  1. Balder ten Cate
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  2. Massimo Franceschet
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Editor information

Editors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD, Oxford, United Kingdom

    Luke Ong

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© 2005 Springer-Verlag Berlin Heidelberg

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ten Cate, B., Franceschet, M. (2005). On the Complexity of Hybrid Logics with Binders. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_24

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  • DOI: https://doi.org/10.1007/11538363_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28231-0

  • Online ISBN: 978-3-540-31897-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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