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Universal deontic modals may vary with respect to whether they scope over or under negation. For instance, English modals like must and should take wide scope with respect to negation; modals like have to and need to take narrow scope. Similar patterns have been attested in other languages. In this article, we argue that the scopal properties of modals with respect to negation can be understood if (a) modals that outscope negation are positive polarity items ( PPIs); (b) all modals originate in a position lower than I 0 ; and (c) modals undergo reconstruction unless reconstruction leads to a PPI-licensing violation.
Iatridou et al. (Tue,) studied this question.