Characterizing Definability of Second-Order Generalized Quantifiers

  • Juha Kontinen
  • Jakub Szymanik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6642)


We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier \({\mathcal{Q}}_1\) is definable in terms of another quantifier \({\mathcal{Q}}_2\), the base logic being monadic second-order logic, reduces to the question if a quantifier \({\mathcal{Q}}^{\star}_1\) is definable in \({\rm FO}({\mathcal{Q}}^{\star}_2,<,+,\times)\) for certain first-order quantifiers \({\mathcal{Q}}^{\star}_1\) and \({\mathcal{Q}}^{\star}_2\). We use our characterization to show new definability and non-definability results for second-order generalized quantifiers. In particular, we show that the monadic second-order majority quantifier Most1 is not definable in second-order logic.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Juha Kontinen
    • 1
  • Jakub Szymanik
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiFinland
  2. 2.Institute of Artificial IntelligenceUniversity of GroningenNetherlands

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