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Stratified reference: the common core of distributivity, aspect, and measurement

Lucas Champollion
From the journal Theoretical Linguistics

Abstract

Why can I tell you that I ran for five minutes but not that I *ran to the store for five minutes? Why can we talk about five pounds of books but not about *five pounds of book? What keeps you from saying *sixty degrees Celsius of water when you can say sixty inches of water? And what goes wrong when I complain that *all the ants in my kitchen are numerous? The constraints on these constructions involve concepts that are generally studied separately: aspect, plural and mass reference, measurement, distributivity, and collectivity. This paper provides a unified perspective on these domains and gives a single answer to the questions above in the framework of algebraic event semantics.

Acknowledgments

A much longer presentation of this theory is offered in Champollion (2010, to appear (b)), a dissertation written at Penn, Stanford, and PARC. This paper was completed at New York University. I am grateful to all these institutions. Special thanks to my advisor, Cleo Condoravdi; my committee members, Aravind Joshi, Maribel Romero, Florian Schwarz; to Sigrid Beck, Danny Bobrow, Lauri Karttunen, Paul Kiparsky, Tony Kroch, Beth Levin, Chris Potts, Anna Szabolcsi, Annie Zaenen, Ziren Zhou; to the participants of my mereology seminar at New York University in 2013 and 2014; to Manfred Krifka, for encouraging me to write this paper; to him and Hans-Martin Gärtner, for their help as editors; to an anonymous reviewer, who provided helpful and detailed suggestions; and to many others who helped me write the dissertation, too numerous to list here.

List of symbols used

ε

a predicate that encodes what it means to be very small

μ

a measure function

σ

the spatial extent function

τ

the runtime function (“temporal trace”)

the mereological sum operator

mereological parthood

*

the algebraic closure operator

|x|

the number of atomic parts of x

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