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I haven't had time to finish my reply to xorxes's comments on
XS3 and XS4.0. But here is the gist of something that takes on
board both xorxes's comments and discussion of KS1.
******
QUANTIFIERS are all underlyingly of the form {N fi'u D}.
If D is {ro(PA)} then Q means "N out of all PA things that are broda".
If D is not {ro(PA)} then ro is still the number of things that
are broda, but Q means "N in every D things that are broda".
Q can be expanded to
( N / D ) * (ro)C
"N in every D of all C=ro things that are broda."
... but I'm not sure how best to Lojban that.
There are three types of value for ro:
su'eci'ino [Individual]
ci'ipa [Bit of (Substance)]
PA-kind = mo'e lo-kind namcu [Substance]
GADCOLUMNS
o-gadri: N fi'u D things that have property 'broda'
e-gadri: a certain N fi'u D things that are described as broda
or: N fi'u D things that have a certain property (described as 'broda')
a-gadri: ro fi'u ro things that have a property that I call 'broda'
GADROWS
I. N1 fi'u D1 things that each are a N2 mei that consists of N2 fi'u
D2 things that have P
II. N1 fi'u D1 things that each are a member of a N2 mei that consists
of N2 fi'u D2 things that have P.
III. (N1 fi'u D1 things that each are) the kind embodying the
property of being a N2 mei that consists of N2 fi'u D2 things
that have P. [D1 is PA-kind]
IV. N1 fi'u D1 things that each are a member of the kind embodying the
property of being a N2 mei that consists of N2 fi'u D2 things
that have P.
V. N1 fi'u D1 things that each are a subkind of the kind embodying the
property of being a N2 mei that consists of N2 fi'u D2 things
that have P. [D1 is ci'ipa]
I can't find any way of doing III without a gadri.[*]
IV can be done as {Q lu'a LO-III}.
V could be done as {Q LO-III}.
II could be done as {Q lu'a pa LO-I}, but *only if* pa has scope over
Q. And it is very much not agreed that this would be so, and it
would doubly controvert the default scoping rules of Lojban (outer
has scope over inner, left has scope over right).
So, aiming for robustness and lexical parsimony, we need LO-I,
LO-II, LO-III.
LO-I corresponds to SL loi/lo'i (lVi/lV'i).
LO-II corresponds to SL lo (lV).
LO-III corresponds to nothing in SL.
Since we need a minimum of 3 gadrows, and SL has exactly 3 gadrows
(not counting the incomplete lV'e), it is tempting, tho not fundie,
to map the 3 SL gadrows to the 3 necessary gadrows. My preferred
mapping is:
LO-I lo'i/le'i/la'i
LO-II loi/lei/lai
LO-III lo/le/la
I know Nick will reject this, but at least we have the gist of a
picture of what a model would do if it were comprehensive, robust
and parsimonious but not necessarily fundie.
[* Doing kind without a gadri: use a cmavo that works like poi'i,
{xoi'i ke'a broda} = "is Mr Broda". Quantify it with PA-kind:
{PA-kind xoi'i ke'a broda}. This gives you lo-kind. As for
le-kind and la-kind, we can suppose that e-gadri and o-gadri
are neutral as to whether they refer to kinds or not. To get
subkinds, use a LAhE, {Q xa'e PA-kind xoi'i ke'a broda}, or
another NU, {Q xoi'oi ke'a broda}.]
ps. In any gadri system, if mo'ezi'o is a possible default, it
should be. We could then define tu'o used as a quantifier to
mean PA-kind.
--And.