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.