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A rethink in the light of minor comments on ExSol 3.0 by
xorxes that had substantial ramifications.
Stuff carried over from the message describing 3.0 is prefixed
by '#>'
Version 4.0
#> 1. No new cmavo are required. (But see 4.)
#>
#> 2. lo'e & le'e aren't really part of the system, and can serve
#> as Nicolaic Prototypes
3. The functions assigned to lV and lVi (and lV'i, for that matter)
could be exchanged. No particular assignment is part of this
proposals, but I will here use the assignment that xorxes favours.
#> 4. SL lV'i is ambiguous between extensionally and intensionally
#> defined sets -- or if it SL lV'i ambiguously means the one then
#> there is no gadri for the other. Extensionally defined sets
#> pattern with extensional [lVi] and Intensionally defined sets
#> with intensional [lV], so one solution (which I prefer) would be
#> to make lo'i/le'i/la'i intensional and add loi'i/lei'i/lai'i for
#> extensional. Another solution would be to use a LAhE that takes a
#> collective as argument and yields a set corresponding to it. In
#> that case, if lu'i were that LAhE, then intensional sets would be
#> {lu'i lo/le/la} and extensional sets would be {lu'i loi/lei/lai},
#> while {lo'i/le'i/la'i} would be by intent ambiguous between
#> extensional and intensional. (NB It cannot be assumed that
#> {lu'i} would be the requisite LAhE; it may be that a new LAhE
#> is required.)
5. KIND.
{lo pa plise} = Mr Single Apple.
{lo re plise} = Mr Pair of Apples.
{lo ro plise} = Mr Collective of All Apples.
{lo pimu plise} = Mr Apple Half.
{lo tu'o plise} = Mr Apple Stuff.
{le pa broda} = a certain Kind embodying what is described as
the property of being a single broda
{le re broda} = a certain Kind embodying what is described as
the property of being a pair of broda
There is no default inner number: when omitted it is glorked from
context, but {lo broda} would normally be glorked as {lo pa broda}
(e.g. for {remna}) or {lo tu'o broda} (e.g. for {djacu}).
{la broda} = Mr Broda
The inner number in a la-phrase is either glorked from context or
is intrinsic to the meaning of the cmene.
There is no implicit outer quantifier on lo/le/la. (IOW, the default
outer quantifier is always mo'ezi'o.)
6. QUANTIFIERS.
All quantifiers are implicitly or explicitly fractional.
{x fi'u y} = "x in every y of"
{(pa) fi'u y} = "1 in every y of"
{ro (fi'u) PA} = "all PA of"
{PA (fi'u ro)} = "PA (out of all) of"
{x (fi'u) ro y} = "x out of all y of"
{ro} is a cardinal number.
{piPA} is a decimalization of {x fi'u y}
{piro} = {ro fi'u ro}
{so'e} = {so'e fi'u ro} = {pi so'e}
{so'i} in {so'i (fi'u ro)} and {piso'i} is defined relative to {ro}.
In {ro (fi'u) so'i} it is defined relative to some glorked standard.
7. {Q lo/le/la broda} = "Q kinds of lo/le/la broda"
{ro} = the total number of Kinds of lo/le/la broda that there are.
8. {Q loi/lei/lai (N) broda = "Q instances of lo/le/la (N) broda".
Instances are extensional; a world with no unicorns contains no
instances of lo unicorn.
There is always a Q. The defaults are:
{(pa fi'u ro) loi/lei/lai broda}
{PA (fi'u ro) loi/lei/lai broda}
{(pa) fi'u PA loi/lei/lai broda}
{ro} = the total number of instances of lo/le/la broda that there are.
However, when N is {tu'o}, there can be no implicit outer quantifier
other than mo'ezi'o (= tu'o). {loi tu'o broda} = "the substance of
all broda". When there is an explicit outer quantifier, it quantifies
over arbitrarily delimited but equal bits of the substance of all
broda.
9. {Q lo'i/le'i/la'i (N) broda} = "Q members of lo/le/la N broda"
The members of lo/le/la broda are intensional. For example,
{lo ci -unicorn}, Mr Unicorn Trio, has three members, regardless
of whether the world contains any unicorns.
There is always a Q. The defaults are:
{(ro fi'u ro) lo'i/le'i/la'i broda}
{PA (fi'u ro) lo'i/le'i/la'i broda}
{(pa) fi'u PA lo'i/le'i/la'i broda}
10. {lo'i Q lV/lVi/lV'i} = "the set containing Q lV/lVi/lV'i (as its
only members)".
{le'i Q lV/lVi/lV'i} = "the set containing a certain Q lV/lVi/lV'i
(as its only members)".
There is no implicit outer quantifier. IOW, the implicit outer
quantifier is mo'ezi'o. There can be an explicit outer quantifier:
{Q1 lo'i/le'i Q2 lV/lVi/lV'i} = "Q1 members of the set containing a certain
Q2 lV/lVi/lV'i (as its only members)".
The defaults for Q1 are the same as given under (9).
11. {loi Q lV/lVi/lV'i} = "the collective containing Q lV/lVi/lV'i",
"Q lV/lVi/lV'i, taken jointly". IOW, in {loi Q lV/lVi/lV'i broda
cu brode}, brodehood belongs to the group collectively rather than
distributively as it would in {Q lV/lVi/lV'i broda cu brode}.
{lei Q lV/lVi/lV'i} = "the collective containing a certain Q
lV/lVi/lV'i (as its only members)".
There is no implicit outer quantifier. IOW, the implicit outer
quantifier is mo'ezi'o. If there is an explicit outer quantifier,
then either it is meaningless or (by stipulation) it means the
same as {Q lo'i/le'i}.
12. {lo Q lV/lVi/lV'i} = "Mr Q lV/lVi/lV'i"
{le Q lV/lVi/lV'i} = "Mr what is described as Q lV/lVi/lV'i", "Mr
A Certain Q lV/lVi/lV'i".
13. {Q loi (N) broda} = {Q broda}. N must be glorked, but is
most likely {pa} or {tu'o}.
#> 14. By stipulation, {piro (loi) broda} and {piso'e (loi) broda} imply
#> inner tu'o.
--And.