Liz Coppock’s research while affiliated with Heinrich Heine University Düsseldorf and other places

... The example here is compatible with both formulations, so I assume the stronger formulation-that the prejacent is the least likely-in my illustration in (28) below. 19 Exclusive particles such as English only are generally treated as presupposing the truth of their prejacent (see, e.g., Horn (1969)), although others treat this as an existential presupposition (that is, that at least one of the alternatives is true; see, e.g., Horn (1996); Geurts and van der Sandt (2004)) or a scalar existential presupposition (roughly, that there is a true alternative that is at least as strong as the prejacent, which in apparently non-scalar examples means entailing the prejacent; see Velleman et al. (2012); Coppock and Beaver (2014)). See also discussion in Crnič (2024). ...

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Focus intervention, multiple association, and the unity of focus and wh alternatives