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Taking ScopeThe Natural Semantics of Quantifiers$
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Mark Steedman

Print publication date: 2011

Print ISBN-13: 9780262017077

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262017077.001.0001

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Distributional Scope of Plurals

Distributional Scope of Plurals

Chapter:
(p.146) (p.147) Chapter 9 Distributional Scope of Plurals
Source:
Taking Scope
Author(s):

Mark Steedman

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262017077.003.0009

Downward distribution of the nonspecific and counting existentials is not possible under generalized quantifier semantics of the nominals since they cannot invert scope. This is evident in the sentences “Some/few/at most two/three boys ate a pizza” and “Some/few/at most two/three farmers who own a donkey feed it.” This chapter illustrates how such downward distributivity arises from the verb. It assumes that, in addition to having the normal translation, many verbs with plural agreement such as read have a “distributivizing” category. The chapter explains that plurals such as “Three boys” translate as set individuals which can be quantified over directly; that is, plural generalized Skolem terms are set-valued. It also considers the proportion problem, counting quantifiers, and distributivity and word order in English and Japanese.

Keywords:   semantics, distributivity, verbs, plurals, Skolem terms, proportion problem, counting quantifiers, word order, English, Japanese

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