Scope-related cumulativity asymmetries and cumulative composition

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.