A remark on collective quantification

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
Categories (categorize this paper)
DOI 10.1007/s10849-007-9055-0
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,692
Through your library
References found in this work BETA
Principles of Mathematics.Bertrand Russell - 1903 - Cambridge University Press.
Language in Action.Johan Van Benthem - 1991 - Journal of Philosophical Logic 20 (3):225-263.
Sums and Quantifiers.Jaap Van Der Does - 1993 - Linguistics and Philosophy 16 (5):509--550.

View all 15 references / Add more references

Citations of this work BETA
Distributivity, Collectivity, and Cumulativity in Terms of (In)Dependence and Maximality.Livio Robaldo - 2011 - Journal of Logic, Language and Information 20 (2):233-271.

Add more citations

Similar books and articles

Monthly downloads

Added to index

2009-01-28

Total downloads

39 ( #130,822 of 2,158,385 )

Recent downloads (6 months)

1 ( #355,511 of 2,158,385 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums