A characterization of monotonicity with collective quantifiers

AbstractThis 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. Unlike previous proposals, one unified determiner fitting operator 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.This research was supported by grant no. 1999210 (“Extensions and Implementations of Natural Logic”) from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. The second author was also partly supported by the fund for the promotion of research at the Technion, research no. 120-042. Part of the research by the second author was curried out during a stay at the Utrecht University, which was supported by an NWO grant no. B30-541. We are indebted to Johan van Benthem for his remarks, which initiated our interest in questions of monotonicity and collectivity. Thanks also to Nissim Francez, Ed Keenan and Shuly Wintner for their comments