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Characterizing Definability of Second-Order Generalized Quantifiers

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Logic, Language, Information and Computation (WoLLIC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6642))

Abstract

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.

The first author was supported by grant 127661 of the Academy of Finland. The second author was supported by NWO Vici grant 277-80-001.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Finland

    Juha Kontinen

  2. Institute of Artificial Intelligence, University of Groningen, Netherlands

    Jakub Szymanik

Authors
  1. Juha Kontinen
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  2. Jakub Szymanik
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Editor information

Editors and Affiliations

  1. Steklov Mathematical Institute, Gubkina 8, 117966, Moscow, Russia

    Lev D. Beklemishev

  2. Centro de Informática, Universidade Federal de Pernambuco, Avenida Prof Luis Freire s/n, Cidade Universitária, 50740-540, Recife, PE, Brazil

    Ruy de Queiroz

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Kontinen, J., Szymanik, J. (2011). Characterizing Definability of Second-Order Generalized Quantifiers. In: Beklemishev, L.D., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2011. Lecture Notes in Computer Science(), vol 6642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20920-8_20

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  • DOI: https://doi.org/10.1007/978-3-642-20920-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20919-2

  • Online ISBN: 978-3-642-20920-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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