If you mean simply "one-some" of a mass with the word "singleton", I agree with you for English "explanation" of {lo PA broda}. As for Lojban "definition", I would rather support the current definition, and need a Lojban definition of {kancu}, which is used in the definition of {zilkancu}.
I suggest as follows:
{x1 kancu x2 x3 x4} =ca'e {gau x1 boi x2 se tcita x3 noi ke'a namcu gi'e x3 mei x4 noi ke'a gradu}
I'm not sure if this definition would be totally reasonable, but at least it mentions {x4 noi ke'a gradu}, consequently {x4 pa mei} because of definition of {gradu}={x1 pa mei gi'e ckaji x3 noi se ckilu x2}.
With this definition, {zilkancu}_3 is clearly defined as {pamei}_1, and no other explanation is necessary.
However, if you mean "individual" with the word "singleton", it is better not to state it, because any mass, no matter if it is used as collective or distributive, can be a unit "one-some" in some sense.
An individual is defined as follows (based on Plural Predication by Thomas McKay, 2006):
"SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}
where RO and DA are not a singular quantifier {ro} and a singular variable {da} of Lojban, but a plural quantifier and a plural variable respectively.
If {zilkancu}_3 should be always an individual, {lo ckafi} is not an individual in many cases of universe of discourse, and it cannot be {zilkancu}_3.
However, {lo ckafi} can be naturally a unit:
{mi cpedu tu'a lo pa ckafi} = {mi cpedu tu'a zo'e noi ke'a ckafi gi'e zilkancu li pa lo ckafi}
This flexibility of {zilkancu}_3, the unit, is advantage of xorlo, and indispensable for keeping expressiveness of Lojban.
No, because the domain of {da} of {da poi (ke'a) su'o (re) mei} spans distributively over plural {su'o (re) mei}_1.
{da poi ke'a gunma cu simxu lo ka prami} treats the plural {simxu}_1 collectively,
just like a developed form of {su'o loi}={su'o da poi ke'a me lo gunma be lo}.
Le mercredi 5 février 2014 16:53:25 UTC+9, la gleki a écrit :
Sorry for intruding. I need to explain this in simple words for a future lojban tutorial.
So
{zo'e} denotes an individual/individuals.
{lo najgenja} = carrot/carrots
{ci lo najgenja cu grake li 60} = {ci zo'e noi najgenja cu grake li 60} - describes carrots. Three of carrots are 60 grams each.
Now I postulate an axiom that {[su'o] lo pa najgenja} describes one carrot (I'll avoid formulae here since i need it for a tutorial, not for a reference grammar).
{ro lo ci najgenja} describes each of the three carrots.
Two important conclusions:
1. {ro lo ci najgenja cu grake li 60} - one carrot is always 60 grams in weight.
2. {ro loi ci najgenja cu grake li 60} = {ro zo'e noi gunma lo ci najgenja cu grake li 60} - describes masses (again of carrots but carrots here are of less importance since carrots are hidden inside gunma2). Each mass of carrots (with three carrots in each mass) is 60 grams so each carrots weighs 20 grams on average.
Yes, it is correct.
I remember someone saying that {lo} is more vague and might include masses as well but here {loi} and it's underlying {gunma} move carrots higher. Can we accept raising here? If yes then all this reasoning immediately breaks.
{lo} can be a mass, but it does not say if the mass satisfies the predicate collectively or/and distributively.
On the other hand, {loi}={lo gunma be lo} says that the mass satisfies the predicate collectively.
When an outer PA is attached to the sumti, the implicit {da} spans distributively over the domain:
{ro lo ci najgenja}={ro da poi me lo ci najgenja}
{ro loi ci najgenja}={ro da poi me lo gunma be lo ci najgenja}
You see, the domain of {ro lo ci najgenja} is each {najgenja}, and that of {ro loi ci najgenja} is each {gunma}.