On the expressive power of monotone natural language quantifiers over finite models

Journal of Philosophical Logic 31 (4):327-358 (2002)

Authors
Jouko A Vaananen
University of Helsinki
Abstract
We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties - here called CE quantifiers - one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantifiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quantification. The notions involved as well as our proofs are presented using a graphical representation of quantifiers in the so-called number triangle
Keywords definability   generalized   monotonicity   quantifiers
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Reprint years 2004
DOI 10.1023/A:1019934611163
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References found in this work BETA

Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Generalized Quantifiers and Natural Language.Jon Barwise - 1980 - Linguistics and Philosophy 4:159.
Questions About Quantifiers.Johan van Benthem - 1984 - Journal of Symbolic Logic 49 (2):443-466.

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Citations of this work BETA

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