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Our paper aims at capturing the distribution of negative polarity items (NPIs) within lexicalized Tree Adjoining Grammar (LTAG). The condition under which an NPI can occur in a sentence is for it to be in the scope of a negation with no quantifiers scopally intervening. We model this restriction within a recent framework for LTAG semantics based on semantic unification. The proposed analysis provides features that signal the presence of a negation in the semantics and that specify its scope. We extend our analysis to modelling the interaction of NPI licensing and neg raising constructions.