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This chapter examines Horn clauses in relation to Negative Inversion. It first considers the properties of the Negative Inversion focus and the Negative Inversion Condition (first and second versions), along with various difficulties for the latter condition. In the sentences A human can know a finite number of primes and A finite number of primes can a human know, a finite number is decreasing in the first case, but the second is still ungrammatical. The chapter also considers a range of expressions with decreasing semantic values for which speakers differ with respect to whether Negative Inversion can be triggered, including cases of decreasing expressions that do not systematically form legitimate Negative Inversion foci but involve the numeral zero, which forms decreasing (in fact, antiadditive) determiner phrases. Finally, it discusses the Negative Inversion Condition (third and fourth versions), the relevance of scope to Negative Inversion, and the implications of quasi-Horn clauses for the Horn clause argument concerning the syntactic nature of Classical NEG Raising (NR).

This chapter examines conditions on topicalization and the way topicalization structures interact with Classical NEG Raising (NR). In the majority of cases, when Negative Inversion is possible for a particular phrase type, topicalization is impossible. However, in cases such as Under no circumstances would I agree to such a plan, Under no circumstances, I would agree to such a plan, Under those circumstances, I would agree to such a plan, and Under those circumstances would I agree to such a plan, the condition on the fronted phrase for topicalization appears to be essentially the negation of the condition on the fronted phrase for Negative Inversion. The chapter considers the Negative Inversion Condition, the Topicalization Condition, Seuren's Highest-Operator Constraint, and sensitivity of the NEG Raising Condition to syntactic islands.

This chapter focuses on certain contexts, dubbed Horn clauses, that demand the syntactic presence of a negative constituent. It first considers fronted negative polarity items (NPIs) by giving examples that represent standard cases of the Negative Inversion construction. The most obvious characteristic of the construction is that the extracted non-wh-constituent in the clause-initial position, termed Negative Inversion focus, co-occurs with subject-auxiliary inversion, which is obligatory. Sentences containing Horn clauses, such as Carl did (not) claim that penguins were mammals and neither did I and Carl claimed that penguins were not mammals (and neither did I), involve syntactic raising of a negation (NEG) from the embedded clause. The chapter proposes for Horn clause cases an analysis that treats examples as resulting from the raising via Classical NR of the NEG. It also shows that Classical NEG Raising (NR) out of Horn clauses is subject to the same set of island constraints holding for non-Horn clause island structures.

This chapter shows that Classical NEG Raising (NR) is sensitive to syntactic islands and considers a range of cases where it is blocked by island constraints, such as those involving clausal complements of nouns. At issue are examples invoking the Complex NP Constraint, clause-internal topics, truth predicates, wh-islands, clause-internal clefts, pseudoclefts, and Negative Inversion. The clear generalization is that Classical NR is never possible from an island. Such a generalization is especially striking for cases where all known semantic conditions on Classical NR are met (for example, for truth predicates), but Classical NR is still not possible. Because syntactic raising phenomena are subject to island constraints, it is possible to account naturally for the above generalization under the assumption that classical NR is a syntactic raising phenomenon. The chapter also examines island types that block strict negative polarity items (NPIs) but not nonstrict NPIs.

This concluding chapter reviews some of the more general theoretical implications of the argument presented in this book with regard to Classical NEG Raising (NR). It first considers the two types of negative polarity items (NPIs), unary-NEG structures and binary-NEG structures (reversals), and the distinction between them, particularly the fact that only unary-NEG NPIs trigger Negative Inversion in Horn clauses. While it is often assumed that natural language negation (NEG) is a clausal modifier (negating the proposition denoted by the clause), this book has described a broad range of English NEG facts with no appeal to clausal negation at all, showing that the standard cases usually taken to motivate English clausal negation actually represent NEGs raised from verbal/adjectival phrases to a position right-adjacent to auxiliary. It has also discussed the idea of quantificational determiner phrase scope positions.