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Complexity of Collective Quantification

  • Jakub SzymanikEmail author
Chapter
Part of the Studies in Linguistics and Philosophy book series (SLAP, volume 96)

Abstract

Generalized quantifier theory tends to focus on distributive readings of natural language determiners. In contrast, this last chapter is devoted to collective readings of quantifiers, e.g., “Most students played poker together”. I start by introducing the common strategy of formalizing collective quantification by using certain type-shifting operations. I show that all these lifts turn out to be definable in second-order logic. Next, I introduce an alternative approach to modeling collective quantification by means of second-order generalized quantifiers and develop a definability theory for them. I study the collective reading of the proportional quantifier ‘most’ and prove that it is not definable in second-order logic. Therefore, there is no second-order definable lift expressing the collective meaning of the quantifier ‘most’. This is clearly a restriction of the type-shifting approach. I finish by discussing various methodological interpretation of this result, touching again upon the issues of complexity in natural language and the semantic borders of everyday language.

Keywords

Collective quantifiers Algebraic approach Type-shifting approach Invariance properties Second-order generalized quantifiers Definability Second-order logic Ristad’s thesis Semantic bounds 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

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