David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Logic, Language and Information 17 (2):131-140 (2008)
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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Livio Robaldo (2011). Distributivity, Collectivity, and Cumulativity in Terms of (In)Dependence and Maximality. Journal of Logic, Language and Information 20 (2):233-271.
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