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.
KeywordsModel Check Modal Logic Model Property Expressive Power Atomic Formula
Unable to display preview. Download preview PDF.
- 2.Bárány, V., Bojańczyk, M.: Finite satisfiability for guarded fixpoint logic. Draft available at arXiv:1104.2262v1 [cs.LO] (2011)Google Scholar
- 3.Bárány, V., Gottlob, G., Otto, M.: Querying the guarded fragment. In: Symposium on Logic In Computer Science, LICS (2010)Google Scholar
- 8.Grädel, E.: Why are modal logics so robustly decidable? Current Trends in Theoretical Computer Science, 393–408 (2001)Google Scholar
- 10.Grädel, E., Walukiewicz, I.: Guarded fixed point logic. In: Proc. LICS 1999. IEEE, Los Alamitos (1999)Google Scholar
- 13.ten Cate, B., Segoufin, L.: Unary negation. In: Proc. STACS 2011 (2011)Google Scholar
- 14.Vardi, M.Y.: Why is modal logic so robustly decidable?. In: Descriptive Complexity and Finite Models, pp. 149–184 (1996)Google Scholar