Journal of Logic, Language and Information

, Volume 17, Issue 2, pp 131–140 | Cite as

A Remark on Collective Quantification

Open Access
Article

Abstract

We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-order logic. We argue that second-order definable quantifiers are probably not expressive enough to formalize all collective quantification in natural language.

Keywords

Collective quantification Lindström quantifiers Second-order generalized quantifiers Type-shifting Definability Computational complexity 

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Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands
  3. 3.Institute of PhilosophyWarsaw UniversityWarsawPoland

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