Guarded Negation

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


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.


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.


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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

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