One defining and yet puzzling feature of linguistic presuppositions is the way they interact with linguistic operators. For instance, when a presupposition trigger (e.g., realise) occurs under negation (e.g., Zoologists do not realise that elephants are mammals), the sentence is most commonly interpreted with the same global presupposition (elephants are mammals) as if negation was not present. Alternatively, the presupposition may be locally accommodated, i.e., the presupposition may become part of what is negated. In this paper, we develop and test two processing accounts of presupposition projection, the global-first model and the local-first model, inspired by dynamic semantics and pragmatic theories respectively. We tested these predic...