NDLI: Monotonicity and Collective Quantification

Content Provider	Springer Nature Link
Author	Ben Avi, Gilad Winter, Yoad
Copyright Year	2003
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.
Starting Page	127
Ending Page	151
Page Count	25
File Format	PDF
ISSN	09258531
Journal	Journal of Logic, Language and Information
Volume Number	12
Issue Number	2
e-ISSN	15729583
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2003-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Logic Artificial Intelligence (incl. Robotics) Semantics
Content Type	Text
Resource Type	Article
Subject	Philosophy Computer Science Linguistics and Language

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