Natural Language Semantics 18 (4):435-470 (2010)

Abstract
The goal of this paper is to propose a unified approach to the split scope readings of negative indefinites, comparative quantifiers, and numerals. There are two main observations that justify this approach. First, split scope shows the same kinds of restrictions across these different quantifiers. Second, split scope always involves low existential force. In our approach, following Sauerland, natural language determiner quantifiers are quantifiers over choice functions, of type <<,t>,t>. In split readings, the quantifier over choice functions scopes above other operators (such as intensional verbs like must or can). Determiner quantifiers leave a choice-function trace when they move and this trace combines with the noun restriction, which is interpreted low. That split scope always involves low existential force is derived, without stipulation, from Kratzer’s idea that low existential force can be achieved via binding (into the noun restriction)
Keywords Split scope  Negative indefinites  Indefinites  Comparative quantifiers  Numerals  Intensional operators  Choice functions  Pseudo-scope
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DOI 10.1007/s11050-010-9060-8
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References found in this work BETA

Choice Functions and the Scopal Semantics of Indefinites.Yoad Winter - 1997 - Linguistics and Philosophy 20 (4):399-467.

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Constraints on the Lexicalization of Logical Operators.Roni Katzir & Raj Singh - 2013 - Linguistics and Philosophy 36 (1):1-29.

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