Some elements in German and English, e.g. every DPs, give rise to cumulativity asymmetries: They allow for cumulative readings only if they occur in the scope of another semantically plural expression. We present a surface-compositional and event-less analysis of this pattern, expanding Schmitt's (2017) 'plural projection' framework. In this system, any constituent containing a semantically plural subexpression denotes a set of (possibly higher-type) pluralities. Cumulativity is built into the rules implementing this 'projection' of semantic plurality.

This paper revisits the semantic variability of sentences with simple plural (in)definites in English and German, which permit distributive, cumulative and paired-cover construals. I argue that this variability reflects context-dependency rather than LF ambiguity (Schwarzschild 1996) and that the selection of a particular construal in context is driven by the QUD in the same way as the choice between maximal and non-maximal construals of plural definites (Malamud 2012; Križ 2015; Križ & Spector 2020). I then develop a new semantics for plural predication on which non-distributive and non-maximal construals form a natural class. The system extends the idea that non-maximality involves truth-value gaps (e.g. Križ 2015) to non-distributive construals by making use of Schmitt’s (2019) ‘plural projection’ framework, in which plural sentences involve special composition rules.

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