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)|
References found in this work BETA
First order predicate logic with generalized quantifiers.Per Lindström - 1966 - Theoria 32 (3):186--195.
A Note on Some Neuroimaging Study of Natural Language Quantifiers Comprehension.Jakub Szymanik - 2007 - Neuropsychologia 45 (9):2158-2160.
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.
Easy Solutions for a Hard Problem? The Computational Complexity of Reciprocals with Quantificational Antecedents.Fabian Schlotterbeck & Oliver Bott - 2013 - Journal of Logic, Language and Information 22 (4):363-390.
On the Identification of Quantifiers' Witness Sets: A Study of Multi-Quantifier Sentences.Livio Robaldo, Jakub Szymanik & Ben Meijering - 2014 - Journal of Logic, Language and Information 23 (1):53-81.
Similar books and articles
Hintikka's Thesis Revisited.Nina Gierasimczuk & Jakub Szymanik - 2007 - Bulletin of Symbolic Logic 13:273.
Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language.Jakub Szymanik - 2010 - Linguistics and Philosophy 33 (3):215-250.
Quantification in English is Inherently Sortal.Ed Keenan - 1999 - History and Philosophy of Logic 20 (3-4):251-265.
A Treatment of Plurals and Plural Quantifications Based on a Theory of Collections.Enrico Franconi - 1993 - Minds and Machines 3 (4):453-474.
Quantifiers in TIME and SPACE. Computational Complexity of Generalized Quantifiers in Natural Language.Jakub Szymanik - 2009 - Dissertation, University of Amsterdam
Characterizing Definability of Second-Order Generalized Quantifiers.Juha Kontinen & Jakub Szymanik - 2011 - 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.
Added to index2009-01-28
Total downloads39 ( #130,822 of 2,158,385 )
Recent downloads (6 months)1 ( #355,511 of 2,158,385 )
How can I increase my downloads?