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We discuss a constraint on global accommodation proposed by Heim stating that an accommodated presupposition must not settle the QUD (Heim, 2015). We argue that this constraint follows from the asymmetry between the pragmatic status of presuppositions and assertions assumed by the satisfaction theory (Stalnaker, 1970; Karttunen, 1964). We provide evidence that local accommodation is sensitive to this constraint, thus arguing that local accommodation maintains the asymmetry. This poses a challenge to theories of local accommodation.
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