Abstract of "Monotonicity and Collective Quantification"
Abstract of "Monotonicity and Collective Quantification"
Gilad Ben-Avi and
Yoad Winter
Journal of Logic, Language and Information 12:127-151.
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This paper studies the monotonicity behavior of plural determiners that quantify over collections. Following previous work, we describe the collective interpretation of determiners such as all, some and most using generalized quantifiers of a higher type that are obtained systematically by applying a type shifting operator to the standard meanings of determiners in Generalized Quantifier Theory. Two processes of counting and existential quantification} that appear with plural quantifiers are unified into a single determiner fitting operator,
which, unlike previous proposals, both captures existential quantification with plural determiners and respects their monotonicity properties.
However, some previously unnoticed facts indicate that monotonicity of plural determiners is not always preserved when they apply to collective predicates. We show that the proposed operator describes this behavior correctly, and
characterize the monotonicity of the collective determiners it derives. It is proved that determiner fitting always preserves monotonicity properties of determiners in their second argument, but
monotonicity in the first argument of a determiner is preserved if and only if it is
monotonic in the same direction in the second argument.
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