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On Sat, Sep 8, 2012 at 7:18 PM, John E Clifford <kali9putra@hidden.email> wrote:
>
> So, you can't just throw in an lV anywhere you want and succeed in saying
> what you want. The same goes for rV and sV, of course, but seems to be more
> critical for lV.
I would say that goes for every word of the language.
> But that is possibly an artifact of my still thinking in
> terms of {lo}, a different sort of operator. Incidentally, if I understand
> what is going on aright, my problems with lV will have repercussions for the
> constants like "I" and "you" and "whatever": if lV is totally leftmost, then
> the first two are all right and the last all wrong; contrariwise
> contrariwise -- well, not really all wrong but "I" and "you" get redefined
> each time they appear.
lV is not totally leftmost, it's just left of its two dependent
formulas. It takes the two formulas that follow it and returns a new
formula, binding any free V that appears in those two formulas. The
meaning of the resulting formula is a predication in which the second
formula is predicated of that which is identified by the first formula
as the value of V. The first formula is not predicated of V, but
serves to identify it.
Now a different issue is the logical transformations or equivalences
between formulas involving l-, r-, s- and other operators. One
equivalence for example is "na lV R P" = "lV R na P". This
transformation contrasts with the corresponding ones for r- and s-,
which are each other's dual: "na sV R P" = "rV R na P" and "na rV R P"
= "sV R na P" . l- is its own dual. Another transformation is "rV1 R1
lV2 R2 P" = "lV2 R2 rV1 R1 P" whenever V1 is not free in R2. Same
thing for s-. All this means that "lV R" can be moved left quite
freely, as long as it doesn't step over a binder of a free variable
found in its restriction.
As for implicitly bound variables, I don't think we bothered yet to
specify where the implicit binder is supposed to go, as it is usually
not very relevant if it's l-, but I would say the rule has to be that
it goes immediately before the simple-formula in which the variable
appears. This means that a'a and e'e will be redefined each time they
appear (unless it's in the same simple-formula), but this can be an
advantage, as you may choose to direct part of your sentence to one
person and another part to another, or one person can complete some
other person's sentence with the personal pronouns getting the right
values.
mu'o mi'e xorxes