lo'ei is xorxes definition of lo'e, used by him for as the definition of lo'e, and used by others to refer to his usage of lo'e. (I have changed the original lo'es to lo'eis for the sake of clarity in the meta-discussion.)
From jboske 398:
I present here my definition of {[lo'ei]} (nothing new, but
maybe better formulated). I don't think it is incompatible
with And's, though the approach is different. I define
it for a very specific case in a specific context, and then
I generalize it.
We start from the official definition of {sisku}:
sisku: x1 seeks/searches/looks for property x2 among set x3
We define a new predicate, {buska}, as follows:
DEF1:
tu'o ka ce'u goi ko'a ce'u goi ko'e ce'u goi ko'i zo'u
ko'a buska ko'e ko'i
cu du tu'o ka ce'u goi ko'a ce'u goi ko'e ce'u goi ko'i zo'u
ko'a sisku tu'o ka ce'u du ko'e kei ko'i
Now we define a particular use of {lo'ei broda} as follows:
DEF2:
buska [lo'ei] broda
= sisku tu'o ka ce'u broda
Notice that from DEF1 we know that:
buska [lo'ei] broda = sisku tu'o ka ce'u du [lo'ei] broda
and from DEF2 we know that:
buska [lo'ei] broda = sisku tu'o ka ce'u du lo broda
So we have that:
tu'o ka ce'u du [lo'ei] broda
= tu'o ka ce'u du lo broda
which does not in any way entail that {[lo'ei] broda} can
be replaced by {lo broda} in other contexts.
In particular, we have:
buska [lo'ei] broda = sisku tu'o ka da poi broda zo'u ce'u du da
buska lo broda = da poi broda zo'u sisku tu'o ka ce'u du da
which are clearly different.
So we have defined {[lo'ei] broda} when it appears in the x2 of
{buska}. To generalize for any context {brode [lo'ei] broda}, we
need a predicate that is to {brode} as {sisku} is to {buska}.
This protopredicate is simply {kairbrode}. It takes a property
in x2 instead of the x2 of brode.
mu'o mi'e xorxes
sisku is defined by the gi'uste as x1 looks for something with property x2. In principle the most natural definition would be x1 looks for object x2, but the actual definition allows searches for non-existent entities, and treats them identically to existent entities. buska, as defined above, is just this second definition x1 looks for object x2. kairbroda is the predicate parallel to sisku for regular predicates; e.g. kaircitka is x1 eats things with property x2.
pycyn has objected (at least at one point or another) to several points about this definition. The ones I can fathom are:
This definition of lo'ei is equivalent in meaning to the second definition of tu'o as a quantifier given on that page (though it may or may not be exactly equivalent in the algebraic formulae that can be applied to it). In other words, in both broda lo'ei brode and broda tu'o brode, there is no quantification over the set lo'i brode; the (intensional) meaning of brode is added to the meaning of broda without actually going and picking out individual brodes (or masses of brodes, etc.)
xorxes has also defined a parallel le'ei, which is his use of le'e.