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Statements about two pluralities can often exhibit weak cumulative readings, with two universal Inferences. One approach encodes cumulativity in the predicate, as a lexical property (e.g. Scha 1984) or as derived from an operator (e.g. Beck & Sauerland 2000). We re-examine the source of cumulativity by looking at the presuppositions of wh-questions that permit cumulative answers. Combining a predicate-based approach to cumulativity with the maximality presupposition of Dayal’s (1996) ANS operator predicts an unattested presupposition. The problem resolves if cumulativity is instead derived from a weak existential meaning via exhaustification, as in Bar-Lev (2020).
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