David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Livio Robaldo (2011). Distributivity, Collectivity, and Cumulativity in Terms of (In)Dependence and Maximality. Journal of Logic, Language and Information 20 (2):233-271.
Similar books and articles
Zachary Ernst & Sara Rachel Chant (2007). Collective Action as Individual Choice. Studia Logica 86 (3):415 - 434.
Juha Kontinen & Jakub Szymanik (2011). Characterizing Definability of Second-Order Generalized Quantifiers. In L. Beklemishev & R. de Queiroz (eds.), Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642. Springer.
Yoad Winter (2003). Monotonicity and Collective Quantification. Journal of Logic, Language and Information 12 (2):127-151.
Jakub Szymanik (2009). Quantifiers in TIME and SPACE. Computational Complexity of Generalized Quantifiers in Natural Language. Dissertation, University of Amsterdam
Enrico Franconi (1993). A Treatment of Plurals and Plural Quantifications Based on a Theory of Collections. Minds and Machines 3 (4):453-474.
Ed Keenan (1999). Quantification in English is Inherently Sortal. History and Philosophy of Logic 20 (3-4):251-265.
Jakub Szymanik (2010). Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language. Linguistics and Philosophy 33 (3):215-250.
Raimo Tuomela (2000). Collective and Joint Intention. Mind and Society 1 (2):39-69.
Nina Gierasimczuk & Jakub Szymanik (2007). Hintikka's Thesis Revisited. Bulletin of Symbolic Logic 13:273.
Gilad Ben-Avi & Yoad Winter (2003). Monotonicity and Collective Quantification. Journal of Logic, Language and Information 12 (2):127-151.
Added to index2009-01-28
Total downloads19 ( #85,584 of 1,096,816 )
Recent downloads (6 months)5 ( #53,739 of 1,096,816 )
How can I increase my downloads?