Presupposition Projection Out of Quantified Sentences: Strengthening, Local Accommodation and Inter-speaker Variation

Presupposition projection in quantified sentences is at the center of debates in the presupposition literature. This paper reports on a survey revealing inter-speaker variation regarding which quantifier yields universal inferences—which Q in QpBqpλx.Cpxqppxqq supports the inference @x P B: ppxq. We observe an implication that if some yields a universal inference for a speaker, no, and any in a polar question do as well. We propose an account of this implication based on a trivalent theory of presupposition projection together with auxiliary assumptions suggested by [8].