Relative quantification and equative scope-taking

Abstract

Relative measure (RM) expressions, e.g., 60% of the olives, are known to be amenable to a non-conservative interpretation, e.g., 60% olivesF, since Ahn & Sauerland (2015a). Herein, I propose an analysis for modified RM phrases with equatives (as much as 60%) and with non-increasing restriction (exactly 60%) that combines a quantificational semantics for proportions (Pasternak & Sauerland 2022) with entity negation for pluralities (Bledin 2024; Elliott 2024). I apply this theory to the novel observation that non-conservative RM phrases can yield a cumulative reading (exactly 2 suppliers sold exactly 60% olivesF), as in van Benthem’s puzzle (Benthem 1986; Brasoveanu 2013; Charlow 2021; a.o.).