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Horn Clauses
Horn clauses, named after the linguist Paul Horn, who discovered the constructions, are clauses which feature that clause complements containing an extracted NPI, triggering subject-auxiliary inversion, and undergoing negative inversion. Take, for example, the following clause Horn heard on the radio, the NPI is highlighted:

"I don't think that ever before have the media played such a major role in a kidnapping."

Syntactic Analysis of Horn Clauses
Collins and Postal define rules that Horn clauses must abide by a few rules:

1. They must be complements.

2. They must be a complement of a CNRP as these manifest a strong reading for main clause negation. (elaborate on strong reading)

The following table shows examples of permitted Horn clauses:

Under the CNRP analysis of Horn clauses, the posited underlying structure does not yet have main clause negation, or negative inversion.

The steps are detailed in the table below:

Negative Polarity Items (NPIs)
Strict NPIs, like breathe a word, require a clause internal licenser. However, negative raising is known to license strict NPIs, as seen in the following example:

Stanley doesn't believe that Carolyn will breathe a word about it

This suggests that the negation originates in the embedded clause, as sister to the VP breathe a word, thus satisfying the locality of selection, being in the embedded clause before participating in raising, moving first to spec CP, and then to its host in the main clause.

Island Constraints
Like other types of movement, Neg-raising is subject to island constraints, suggesting that they must raise from the embedded clause into the main clause.

Wh- Islands
Neg-raising is not permitted in wh- islands. Consider the following examples, where negation is only permitted in the embedded clause and not the main clause, despite the ability of negation in the main clause to license NPIs: This can be explained by the wh- word how undergoing movement first, filling the space in spec CP. Once this happens, negation can no longer participate in cyclic movement by stopping in spec CP before moving to the main clause. The result of violating the cyclic movement gives us the ungrammatical sentence.