“…But this traditional meaning, when combined with the standard e, e, t interpretation of transitive verbs, actually fails to account for a cumulative reading of every-DPs regardless of the syntactic configuration. As alluded to above, there are different semantic analyses that are compatible with a structural approach to cumulativity asymmetries, and each of them deviates in some way from the assumptions about LF syntax that lead to a type mismatch: Event-based approaches (Ferreira, 2005;Chatain, 2020Chatain, , 2022 analyze lexical verbs as denoting unary predicates of events regardless of their arity, and every-DPs as operators on such predicates (possibly mediated by a thematic-role operator); Champollion (2010) analyzes every-DPs not as quantifiers, but as simple type e plurals that must stand in a certain syntactic relation to a cumulation or distributivity operator; and Haslinger and Schmitt (2018) interpret predicates as sets of pluralities (as opposed to simple relations between individuals) and provide a cross-categorial schema to interpret every-DPs as operators on such sets. Finally, in Sect.…”