EE connects adverbs to other adverbs. Some adverbs can
modify other adverbs ("very", "quite"); these carry EE+
connectors. Adverbs which can be modified in this way (some
can not) take EE-.

           +---MVa---+
	   |    +-EE-+
	   |    |    |
	I ran very quickly	

EE can also be used with E ("He very quickly left"), CO
("Very quickly, he left") and EB ("He is very clearly a
good programmer"). 

EEh: Adverbial questions
EEh is used to connect "how" to adverbs, in adverbial
questions (direct or indirect): "How quickly did you run", "I
wonder how quickly you ran". Adverbs that can be used in
questions like this thus take "{EE-} & (Qe+ or Ca+ or
MVa-...)".  "Qe" is used in direct questions; "Ca" is used in
indirect questions.

                     +---I---+
         +EEh-+--Qe--+-SI+   |
         |    |      |   |   |
	How quickly did you run

EEh is therefore analagous to EAh (see "EAh"). The use of EEh
is constrained by post-processing in a very similar way. The
"EE-" on adverbs is conjoined with MVa-; thus an adverb might,
in principle, make both an EEh and an MVa connection: "*I ran
how quickly". In practice, however, EEh is only usable with
Qe+ (used in direct questions) and Ca+ (in indirect
questions). EEh+ on "how" is conjoined with "R- or Wq- or
Ws-".  When EEh is used with MVa, either "how" cannot make the
connection it needs to the left, or else the bounded-domain
constraint is violated. See "EAh".

How Much, How Much More
"Much" can also be used with "how" as a determiner or
noun-phrase (see "H").  It can also make an EC+ connection to
"more"; "more" may then act as a noun-phrase (ex.1) or as a
determiner. Alternatively, "more" can act as a comparative
adverb modifying a sentence or a following adjective.  In this
case, however, a different linkage is used (ex.2 & 3):

         +--H-+ECn+
         |    |   |
     1.	How much more did you earn

         +EEh-+ECa+
         |    |   |
     2.	How much more can you run
     3.	How much more efficient is your program		

In either case, "how" makes a W connection to the wall (in
direct questions) or an QI connection in indirect question. In
that case, why do we distinguish between "H" and "EEh" at all?
The reason is that there are complex constraints on the way
this phrase is used. Consider the following:

	1. How much more money do they have
	2. How much more money will be coming in
	3. How much more efficient is their program
	4. *How much more efficient programmers do they have
	5. How much more efficient a programmer do they have
        6. *How much more efficient programmers work for them
	7. *How much more efficient a programmer works for them

A pattern emerges here, similar to the pattern that emerged with
"EAh":

	8. How many dogs did you chase
	9. How many dogs chased you
	10. How big is it
	11. *How big dogs did you chase
	12. How big a dog did you chase
	13. *How big dogs chase you
	14. *How big a dog chased you

When the focus of the question is an adjective, either
directly or indirectly ("How efficient", "How much more
efficient"), then it must be a "be"-type ("AF") question; it
may not be a a subject- ("S") or object-type ("B") question;
the exception is object-type singular questions like ex. 12
("How big a dog"). Exs. 8 and 9 are not adjective-focused;
ex. 10 contains an "AF" link; thus these are fine.  We already
have a mechanism for ensuring that in adjective-focused
questions like 10-14, an AF link must occur, except in cases
like ex. 12. (see "EAh".)  Thus the constraints are set up
just the way we want: we just have to find a way of triggering
them in the right cases, i.e., in "adjective-focused
questions"; ex. 3-7 above.  The problem is that in cases 8-14,
adjective-focused questions are easily characterized; they all
contain an "EAh".  With exs. 1-7, they are not so easily
characterized.  We need to make sure that the
adjective-focused questions, and these only, all contain a
certain link-type. Then we can have that link trigger the same
the same constraints that are triggered by EAh.  This we do
through connector logic; the link we use is EEh. (Irrelevant
connectors and subscripts are omitted here.)

        how: (QI- or W-) & (H+ or EEh+);
	much: (H- & (ECn+ & Dmu+)) or (EE- & (ECa+))
	more: (ECn- & (Dmu+ or S+ or B+)) or (ECa- & EA+)

If "more" forms an EA+ link with an adjective - implying an
adjective-focused question - an ECa link with "much" is
required; an EEh link with "how" is then formed (if any link
with "how" is formed); and the "adjective-focused question"
constraints are applied. Thus 4, 6, and 7 above are
prohibited; 3 and 5 are allowed.  However, if "more" is acting
as a determiner or noun-phrase (as in 1 and 2 above), its ECn+
connector is used; the ECn- on "much" is therefore used, a H
link with "how" is formed, and the "adjective-focused
question" constraints are not enforced.

(Recall that EEh, as well as being used in adjective-focused
comparative questions, is also used in adverbial questions:
"How quickly did he do it?" Thus Ca and Qe - which occur in
adverbial questions - are added to the list of "contains_one"
links that EEh requires in its group.  Notice also that "How
much more" may be used in yet another way as an adverbial
phrase: "How much more did he do it?" Thus "more", like other
adverbs, must carry "Qe+ and Ca+" conjoined with its ECa-.
Further, "more" may itself modify an adverb: "How much more
quickly did he do it?" Thus "more" must also carry EE+, like
other adverb-modifying adverbs.)

EAx connects certain adverbs to the word "many", when it
is not being used in questions. The adverbs that can
modify adjectives ("very", "relatively") can also
modify "many". EA is also used by "how" to connect to
adjectives; "how" has "EAh+" for this purpose. However, 
"EAh" has a special use in post-processing: it signifies
that an adjective-focused question is present (see EAh).
To prevent such connections from forming in the phrase
"how many", we give "many" an EEx- connector and create
a H link for linking "how" and "many". 

EExk is used in the constructions "so [adverb]...that" and "so
much...that". See "EAxk: so...that".  Other EE subscripts
relate to comparatives; see "MV: Comparatives", sections I
(EEm) and VII (EEy).