Journal of Logic, Language and Information

, Volume 18, Issue 4, pp 493–514 | Cite as

The Complexity of Hybrid Logics over Equivalence Relations

Article

Abstract

This paper examines and classifies the computational complexity of model checking and satisfiability for hybrid logics over frames with equivalence relations. The considered languages contain all possible combinations of the downarrow binder, the existential binder, the satisfaction operator, and the global modality, ranging from the minimal hybrid language to very expressive languages. For model checking, we separate polynomial-time solvable from PSPACE-complete cases, and for satisfiability, we exhibit cases complete for NP, PSpace, NExpTime, and even N2ExpTime. Our analysis includes the versions of all these languages without atomic propositions, and also complete frames.

Keywords

Hybrid logic Downarrow operator Satisfiability Model checking 

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References

  1. Areces, C., Blackburn, P., & Marx, M. (1999). A road-map on complexity for hybrid logics. In Proceedings of the 13th CSL, 1999, volume 1683 of LNCS (pp. 307–321). Springer.Google Scholar
  2. Areces C., Blackburn P., Marx M. (2000) The computational complexity of hybrid temporal logics. Logic Journal of the IGPL, 8(5): 653–679CrossRefGoogle Scholar
  3. Blackburn P., Seligman J. (1995) Hybrid languages. Journal of Logic, Language and Information, 4: 251–272CrossRefGoogle Scholar
  4. Blackburn, P. & Seligman, J. (1998). What are hybrid languages? In M. Kracht, M. de Rijke, H. Wansing, & M. Zakharyaschev (Eds.), Advances in Modal Logic, volume 1 of CSLI Publications (pp. 41–62). Stanford University.Google Scholar
  5. Chlebus B.S. (1986) Domino-tiling games. Journal of Computer and System Sciences, 32(3): 374–392CrossRefGoogle Scholar
  6. Franceschet M, de Rijke M. (2005) Model checking for hybrid logics (with an application to semistructured data). Journal of Applied Logic, 4(3): 279–304CrossRefGoogle Scholar
  7. Franceschet, M., de Rijke, M., & Schlingloff, B.-H. (2003). Hybrid logics on linear structures: Expressivity and complexity. In Proceedings of the 10th TIME, 2003 (pp. 166–173). IEEE Computer Society.Google Scholar
  8. Goranko V. (1996) Hierarchies of modal and temporal logics with reference pointers. Journal of Logic, Language and Information, 5(1): 1–24CrossRefGoogle Scholar
  9. Ladner R.E. (1977) The computational complexity of provability in systems of modal propositional logic. SIAM Journal on Computing, 6(3): 467–480CrossRefGoogle Scholar
  10. Lange, M. (2005). A lower complexity bound for propositional dynamic logic with intersection (Vol. 5, pp. 133–147). King’s College Publications.Google Scholar
  11. Mundhenk, M., Schneider, T., Schwentick, T., & Weber, V. (2005). Complexity of hybrid logics over transitive frames. In H. Schlingloff (Ed.), M4M, volume 194 of Informatik-Berichte (pp. 62–78). Humboldt-Universität zu Berlin. The cited version is http://arxiv.org/abs/0806.4130v1atarXiv.or.
  12. Papadimitriou, C. H. (1994). Computational complexity. Addison-Wesley.Google Scholar
  13. SavelsberghM.vanEmde Boas P. (1984) Bounded tiling, an alternative to satisfiability. In: Wechsung G. (eds) 2nd Frege Conference, volume 20 of Mathematische Forschung.. Akademie Verlag, Berlin, pp 354–363Google Scholar
  14. ten Cate, B., & Franceschet, M. (2005). On the complexity of hybrid logics with binders. In Proceedings of the 19th CSL, 2005, volume 3634 of LNCS (pp. 339–354). Springer.Google Scholar
  15. Vardi, M., & Stockmeyer, L. (1985). Improved upper and lower bounds for modal logics of programs. In Proceedings of the 17th STOC (pp. 240–251).Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institut für InformatikFriedrich-Schiller-UniversitätJenaGermany
  2. 2.School of Computer ScienceUniversity of ManchesterManchesterUK

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