**Speaker: ** Nina Haslinger (University of Göttingen)**Title: **Cumulativity as global non-maximality: A non-lexical underspecification approach**Time: **Wednesday, May 19th, 1pm – 2pm**Abstract: **In this talk, I argue that cumulative construals of sentences with multiple plurals (e.g. a construal of (1) that only requires the existence of a plurality of two students such that each of them read books and each book was read by at least one of them) are subject to contextual constraints that parallel those for non-maximal construals of plural definites (e.g. a construal of (2) on which not all of the windows have to be open). In particular, the QUD-dependence observed for non-maximal construals (Malamud 2012, Križ 2015 a.o.) and their sensitivity to contextual alternatives of the predicate (Križ 2015) carry over to cumulativity.

(1) Two of my students have read all the books. (2) The windows are open.

Since cumulativity does not literally reduce to non-maximality, a unified approach to both phenomena is needed. Existing arguments against an ambiguity approach to non-maximality can be extended to argue that (1) should not have separate LFs for the distributive and the cumulative reading (cf. Schwarzschild 1996, Kratzer 2008). In simple cases like (1), the context-dependency behavior of cumulativity can be accounted for by a straightforward extension of the three-valued approach to non-maximality, so that (1) expresses a three-valued proposition that is neither true nor false in a cumulative scenario.

I then show that this approach will not extend to all cases of cumulativity, based on German data involving plurals within an embedded clausal conjunction (cf. Schmitt 2019). The problematic cases are analyzed within a variant of Schmitt’s (2019) system in which any expression containing a plural denotes a predicate of pluralities (possibly of higher type). To account for the context-dependence of cumulative and non-maximal construals, I propose that these predicates of pluralities should be three-valued, with ‘classical’ and ‘tolerant’ extensions that are computed in parallel. Plural sentences end up denoting a three-valued predicate of propositions, which leads to a gap between the truth conditions and the falsity conditions that is resolved in a QUD-dependent manner. I conclude by outlining some potential advantages of this system over the standard ambiguity approach to cumulative and distributive construals.