Constraints on distributivity
Creators: name: Law, Hoi Ki
Publisher: name: No Publisher Supplied
Year: 2019

description: Distributivity can be marked with lexical items like binominal each in English:(1) The girls read three books each.It has long been noted that some distributivity markers need to be licensed by the morphosyntactic makeup and/or interpretive properties of the predicate being distributed over (e.g, read three books in (1)). In this dissertation I investigate three distributivity markers that exhibit this type of licensing requirement:1. binominal each in English (Safir and Stowell 1988, Zimmermann 2002, Champollion 2015, Kuhn 2017);2. the verbal distributivity suffix saai in Cantonese (Tang 1996, Lee 2012);3. the adverbial distributivity marker ge in Mandarin (Kung 1993, Lin 1998b, Lee et al. 2009a).The investigation leads to two findings. The first finding is that these licensing requirements should be understood as constraints on the dependencies arising from distributive quantification, which echo similar constraints proposed for various types of indefinites (Farkas 1997, 2002b, Brasoveanu and Farkas 2011, Henderson 2014, Kuhn 2017). A consequence of this finding is a more general conception of constraints on dependencies: they are not only associated with indefinites (as con- ceived of in Farkas (2002b)), as they may be borne by distributivity markers.The second finding is that constraints on dependencies may differ along a few parameters. One parameter determines whether a constraint makes reference to the internal mereological structure of dependencies, which arise from evaluating distributivity. Using the interactions of distributiv- ity markers with extensive and intensive measure phrases (Zhang 2013), I conclude that the con- straints under investigation make reference to the mereological nature of distributive dependencies. These constraints stand in contrast with constraints previously formulated for dependent indefinites (Farkas 1997, 2002b, Henderson 2014, Champollion 2015, Kuhn 2017), which do not need to access the mereological structure of dependencies. Another parameter determines whether a constraint re- quires dependence or independence. Using the contrast between binominal each and Mandarin ge on the one hand, and Cantonese saai on the other hand, I show that both parameters are used in natural language. This conclusion adds further support to the parallelism between constraints contributed by distributivity markers and those contributed by indefinites, as the dependence-independence pa- rameter has also been used to characterize dependent indefinites and specific indefinites (e.g., Farkas 2002b, von Heusinger 2002).To make constraints on dependencies formally explicit, I devise a version of dynamic plural logic with features from van den Berg (1996) and Brasoveanu (2008, 2013) to semantically represent dependencies arising from evaluating distributive quantification. The use of a dynamic logic, cou- pled with a delayed evaluation mechanism in terms of higher order meaning (Cresti 1995, de Swart 2000, Charlow (to appear)), allows the constraints to act as output constraints on distributive quan- tification, which mirror the use of output constraints in studies like Farkas (1997, 2002b), Henderson 2014, and Kuhn (2017).