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H connects "how" to "much" or "many". "Much" and "many" can serve
as determiners ("How many books do you have"); they can also
serve as independent noun-phrases ("How many do you have").
Unlike most determiners, they can also be preceded by the word
"how" in either case, creating a question or indirect
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How many books do you have
Therefore they have H- connectors, optionally conjoined with
their D+ connectors and also with their main noun
complexes. However: when the H- is being used on "many" and
"much", a question situation is created (direct or
indirect). This introduces constraints on word-order, mainly
relating to subject-verb inversion. For this reason, H+ on
"how" is conjoined with QI- (used in indirect questions) or
Wq- or Ws- (used in direct questions). These connectors
trigger post-processing rules; see "SI". "H" is also in a
post-processing category along with "D##w", relating also to
s-v inversion; see "SI: Questions without s-v inversion".
Grammar Documentation Page.