Almost All Complex Quantifiers Are Simple

  • Jakub Szymanik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6149)


We prove that PTIME generalized quantifiers are closed under Boolean operations, iteration, cumulation and resumption.


generalized quantifiers computational complexity polyadic quantifiers Boolean combinations iteration cumulation resumption 


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  1. 1.
    Peters, S., Westerståhl, D.: Quantifiers in Language and Logic. Clarendon Press, Oxford (2006)Google Scholar
  2. 2.
    van Benthem, J.: Essays in logical semantics. Reidel, Dordrecht (1986)MATHGoogle Scholar
  3. 3.
    Mostowski, M.: Computational semantics for monadic quantifiers. Journal of Applied Non-Classical Logics 8, 107–121 (1998)MATHMathSciNetGoogle Scholar
  4. 4.
    McMillan, C.T., Clark, R., Moore, P., Devita, C., Grossman, M.: Neural basis for generalized quantifier comprehension. Neuropsychologia 43, 1729–1737 (2005)CrossRefGoogle Scholar
  5. 5.
    Szymanik, J., Zajenkowski, M.: Comprehension of simple quantifiers. Empirical evaluation of a computational model. Cognitive Science 34(3), 521–532 (2010)CrossRefGoogle Scholar
  6. 6.
    Mostowski, M., Wojtyniak, D.: Computational complexity of the semantics of some natural language constructions. Annals of Pure and Applied Logic 127(1-3), 219–227 (2004)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Sevenster, M.: Branches of imperfect information: logic, games, and computation. PhD thesis, Universiteit van Amsterdam (2006)Google Scholar
  8. 8.
    Szymanik, J.: Quantifiers in TIME and SPACE. Computational Complexity of Generalized Quantifiers in Natural Language. PhD thesis, Universiteit van Amsterdam (2009)Google Scholar
  9. 9.
    Gierasimczuk, N., Szymanik, J.: Branching quantification vs. two-way quantification. Journal of Semantics 26(4), 367–392 (2009)CrossRefGoogle Scholar
  10. 10.
    Szymanik, J.: The computational complexity of quantified reciprocals. In: Bosch, P., Gabelaia, D., Lang, J. (eds.) LNCS (LNAI), vol. 5422, pp. 139–152. Springer, Heidelberg (2008)Google Scholar
  11. 11.
    Kontinen, J., Szymanik, J.: A remark on collective quantification. Journal of Logic, Language and Information 17(2), 131–140 (2008)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Frixione, M.: Tractable competence. Minds and Machines 11(3), 379–397 (2001)MATHCrossRefGoogle Scholar
  13. 13.
    Immerman, N.: Descriptive Complexity. In: Texts in Computer Science, Springer, Heidelberg (1998)Google Scholar
  14. 14.
    Papadimitriou, C.H.: Computational Complexity. Addison Wesley, Reading (November 1993)Google Scholar
  15. 15.
    van Benthem, J.: Polyadic quantifiers. Linguistics and Philosophy 12(4), 437–464 (1989)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Hella, L., Väänänen, J., Westerståhl, D.: Definability of polyadic lifts of generalized quantifiers. Journal of Logic, Language and Information 6(3), 305–335 (1997)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jakub Szymanik
    • 1
  1. 1.Department of PhilosophyUtrecht UniversityUtrechtThe Netherlands

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