Advertisement

Guarded Negation

  • Vince Bárány
  • Balder ten Cate
  • Luc Segoufin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)

Abstract

We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend the guarded fragment of first-order logic and guarded least fixpoint logic, respectively. They also extend the recently introduced unary negation fragments of first-order logic and of least fixpoint logic.

We show that the satisfiability problem for GNFO and for GNFP is 2ExpTime-complete, both on arbitrary structures and on finite structures. We also study the complexity of the associated model checking problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also model theoretically: we show that GNFO and GNFP have the tree-like model property and that GNFO has the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an appropriate notion of bisimulation.

Keywords

Model Check Modal Logic Model Property Expressive Power Atomic Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andréka, H., van Benthem, J., Németi, I.: Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic 27, 217–274 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Bárány, V., Bojańczyk, M.: Finite satisfiability for guarded fixpoint logic. Draft available at arXiv:1104.2262v1 [cs.LO] (2011)Google Scholar
  3. 3.
    Bárány, V., Gottlob, G., Otto, M.: Querying the guarded fragment. In: Symposium on Logic In Computer Science, LICS (2010)Google Scholar
  4. 4.
    Berwanger, D., Grädel, E.: Games and model checking for guarded logics. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS (LNAI), vol. 2250, p. 70. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Bojańczyk, M.: Two-way alternating automata and finite models. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, p. 833. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Grädel, E.: Decision procedures for guarded logics. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 31–51. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Grädel, E.: On the restraining power of guards. J. Symb. Logic 64(4), 1719–1742 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Grädel, E.: Why are modal logics so robustly decidable? Current Trends in Theoretical Computer Science, 393–408 (2001)Google Scholar
  9. 9.
    Grädel, E., Otto, M., Rosen, E.: Undecidability results on two-variable logics. Arch. Math. Log. 38(4-5), 313–354 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Grädel, E., Walukiewicz, I.: Guarded fixed point logic. In: Proc. LICS 1999. IEEE, Los Alamitos (1999)Google Scholar
  11. 11.
    Libkin, L.: Elements of Finite Model Theory. Springer, Heidelberg (2004)CrossRefzbMATHGoogle Scholar
  12. 12.
    Mortimer, M.: On languages with two variables. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 21(8), 135–140 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    ten Cate, B., Segoufin, L.: Unary negation. In: Proc. STACS 2011 (2011)Google Scholar
  14. 14.
    Vardi, M.Y.: Why is modal logic so robustly decidable?. In: Descriptive Complexity and Finite Models, pp. 149–184 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Vince Bárány
    • 1
  • Balder ten Cate
    • 2
  • Luc Segoufin
    • 3
  1. 1.University of WarsawPoland
  2. 2.UC Santa CruzUSA
  3. 3.INRIA and ENS Cachan, LSVFrance

Personalised recommendations