Abstract
This article studies the monotonicity behavior of plural determinersthat quantify over collections. Following previous work, we describe thecollective interpretation of determiners such as all, some andmost using generalized quantifiers of a higher type that areobtained systematically by applying a type shifting operator to thestandard meanings of determiners in Generalized Quantifier Theory. Twoprocesses of counting and existential quantification thatappear with plural quantifiers are unified into a single determinerfitting operator, which, unlike previous proposals, both capturesexistential quantification with plural determiners and respects theirmonotonicity properties. However, some previously unnoticed factsindicate that monotonicity of plural determiners is not always preservedwhen they apply to collective predicates. We show that the proposedoperator describes this behavior correctly, and characterize themonotonicity of the collective determiners it derives. It is proved thatdeterminer fitting always preserves monotonicity properties ofdeterminers in their second argument, but monotonicity in the firstargument of a determiner is preserved if and only if it is monotonic inthe same direction in the second argument. We argue that this asymmetryfollows from the conservativity of generalized quantifiers innatural language.
Keywords collectivity  determiner  generalized quantifier  monotonicity  plural  type shifting
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DOI 10.1023/A:1022305918225
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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.

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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.
Perspectival Plurality, Relativism, and Multiple Indexing.Dan Zeman - 2018 - In Rob Truswell, Chris Cummins, Caroline Heycock, Brian Rabern & Hannah Rohde (eds.), Proceedings of Sinn und Bedeutung 21, Vol. 2. Semantics Archives. pp. 1353-1370.
A Remark on Collective Quantification.Juha Kontinen & Jakub Szymanik - 2008 - Journal of Logic, Language and Information 17 (2):131-140.
Pragmatic Identification of the Witness Sets.Livio Robaldo & Jakub Szymanik - 2012 - Proceeding of the 8th Conference on Language Resources and Evaluation.

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