The two types are not equivalent as answers to questions: while the [XP no] type can be considered the unmarked one, the [no XP] type typically has a corrective feel to it. I discuss this difference in section 2, where I argue it can be reduced to the topic/focus status of the remnant XP. After this, I turn to the syntactic derivation. I will argue that both types of replies stem from an underlying full clause that undergoes PF deletion. In addition, I will suggest that, in certain contexts, the [no XP] type can be given an alternative, non-elliptical derivation. The rather interesting conclusion is that “constituent negation” is not a unified construction (cf. Etxepare n.d., who reaches the same conclusion on independent grounds). Rather, the exact structure of [no XP] fragments depends on the finer properties of the string in question.
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