Quantifier Scope Problem Solved!

[John Cowan <cowan@ccil.org>]

I was reflecting on the problem of quantifier scope in Lojban
reflected by the English sentence "Two dogs bite three men".
The translation

1)	le re gerku cu batci le ci nanmu
	The two dogs bit the three men.

means that there are two dogs and three men in the speaker's mind,
and that each of the dogs bites each of the men, for six acts of
biting altogether.  No problem here.

The translation

2)	re lo gerku cu batci ci lo nanmu
	Two dogs bite three men.

means that there are two dogs (out of the complete set of dogs) and
six acts of biting, but the number of men may vary from three to
six, depending on how the overlap happens to work, because Example 2
is equivalent to:

3)	re da poi gerku ci de poi nanmu zo'u da batci de
	For-two X which are-dogs, for-three Y which-are men, X bites Y

Reversing the two variable bindings gives us three men, but from two
to six dogs.  How do we, without introducing the specific article
"le", get exactly two dogs and three men?

I had proposed the artificial use of termsets for this purpose:

5)	nu'i re da poi gerku ci de poi nanmu nu'u zo'u da batci de

or with less machinery

6)	nu'i re lo gerku ci lo nanmu nu'u cu batci	(forethought)
	re lo gerku ce'e ci lo nanmu cu batci		(afterthought)

but certain disadvantages result.  We needed a grammar change to make
termsets without a connective grammatical (and to add afterthought
termset machinery with "ce'e"), and we can't split the termset
around the selbri for SVO order.

Now I think I see a resolution to the problem.  Use

7)	ro lo re lo gerku cu batci ro lo ci lo nanmu
	Each-of two dogs bites each-of three men.

Now the quantifiers of the two sumti are universal, so order doesn't
matter: we get the right results even if the sumti are swapped around
in a prenex.  Furthermore, we get a general theory of what
LE+quantifier+sumti
means:

8)	ro lo re lo gerku

is the same as

9)	ro lo me re lo gerku
	ro da poi me re lo gerku

(using the new definition of "me" that makes it true of everything
described
by the sumti that it governs).

Comments?

Partly separate issue:  lojbab pointed out that afterthought termset
logical
connection like

10)	la djan ce'e la meiris. pe'eje la frank. ce'e la eimis. cu prami
	John Mary and Frank Amy loves.

isn't very "afterthought", because you have to have used the "ce'e" to
create
the termset before you can logically connect it.  The only two other
applications
of termsets are the quantifier-scope use above, and a proposal to solve
the
"tense magnitude" problem thus:

11)	la djan. zu'a la frank. ce'e sela'u lo mitre be li mu cu cadzu le
bisli
	John to-the-left-of (Frank in-quantity is-in-meters 5) walks on-the ice
	John walks on the ice five meters leftward of Frank.

where the termset allows both the origin point and the magnitude to be
governed
by the sumtcita "zu'a" = "left-of".  I forgot about this use, so it
isn't yet in
the reference grammar.

Is the grammatical change required to add connective-less termsets and
afterthought
termsets with or without connections still required in the light of the
first half
of this message?

-- 
John Cowan						cowan@ccil.org
			e'osai ko sarji la lojban