Re: [lojban] Re: tersmu 0.2

On Mon, Oct 20, 2014 at 10:06 PM, Martin Bays <mbays@sdf.org> wrote:

* Saturday, 2014-10-18 at 22:27 -0300 - Jorge Llambías <jjllambias@gmail.com>:
>
> And if we take them as primitive, the strange thing is that they form
> a small closed class, so you could not do with most functions what you
> could do with them.

Could you rephrase that? I don't see what you mean.

Not sure what I meant now. I think I meant that you couldn't do with most functions (i.e. lo-functions) what you could do with the closed class of LAhE-functions, in terms of scope. (You can do it indirectly by using the prenex, of course.)

But anyway: technically the class isn't actually closed, because of {na'u}!

Would "na'u broda" be an open class of functions but not "lo broda"? "na'u" seems to be an inside-of-mex equivalent of "lo". We could say that "lo broda"="li na'u broda mo'e zo'e/zi'o".

There are also scope questions. Probably we don't want
{ro danlu cu jbena gi'e ba bo morsi} to be equivalent to
{ro danlu cu jbena .i ba bo ro danlu cu morsi}?

"ro danlu" has scope over "gi'e" so it would be:

ro da poi danlu zo'u ge ge da jbena gi da morsi gi lo nu da morsi cu balvi lo nu da jbena

If the logical connective isn't {je}, probably the tag relation should
only apply when the connectands are both true, i.e. corresponding
events/facts occur/hold. This seems sensible, and is supported by CLL
Chapter 10 Verse 17.10.

So ".i je nai [tag] bo" is always false? I never could make much sense of "tag bo" with connectives other than "je".

Firstly, we need a way to assign an event/fact variable to a proposition
without changing its semantics. {fi'o du} lets us do this; {fi'o du ko'a
broda} means that broda occurs/holds and ko'a is equal to the
event/fact of this. Let's make this a primitive in the logic, writing it
as "=.", so e.g. "{ko'a}=. broda()". (So technically "[term]=." is
a modal operator.)

I had never considered "fi'o du", it sounds useful. Maybe we want "fi'o ca'e du" if it's an assignment to a variable, rather than a claim. Or maybe it should be "sei ca'e ko'a du'u no'a", although I'm not sure whether "no'a" gets the right bridi.

(I write the above paragraph as if I'm sure it makes sense, but I'm not.
If there are many events of brodaing in the situation, is {fi'o du ko'a
broda} true when ko'a is any of those events, or only when it's the
"intended" one?

I would say it assigns to "ko'a" the intended ones, i.e. the ones you are describing with this proposition.

The below makes sense in either case, but with subtly
different results. If instead tags work such that {fi'o du ko'a broda}
isn't true for *any* ko'a in such a situation, then there's a problem!)

If there's no referent to assign to ko'a, the assignment will fail in the same way that a "goi" assignment could fail

Then we can handle tagged conjunction by quantifying over events:
ro danlu cu jbena gi'e ba bo morsi ->
FA x1:(danlu(_)). EX x2. (x2=. jbena(x1) /\ (ba)(x2). morsi(x1))
ro da poi ke'a danlu ku'o su'o de zo'u ge fi'o du de zo'u da jbena
gi ba de zo'u da morsi
, which is I think a natural and useful way to interpret it.

To be clear, that's intended to be equivalent to the following more
symmetric form:
FA x1:(danlu(_)). EX x2. EX x3. ((x2=. jbena(x1) /\ x3=. morsi(x1))
/\ {ba}(x2,x3))
ro da poi danlu ku'o de di zo'u ge ge fi'o du de da jbena gi fi'o du
di da morsi gi de xo'i ba di

Now for connectives other than conjunction, I'm not seeing a neater
solution than to "skim off" the TT case (if there is one); so e.g. to
consider {broda .i na ja ba bo brode} to be equivalent to
{ na broda .i ja broda .i je ba bo brode}, where the tagged conjunction
is interpreted as above.

Not very pretty. I'd be happy to hear of alternative possibilities.

(When working on tersmu, I somehow convinced myself that the above
handling of tagged conjunction would go through unchanged for other
tagged connectives. So that's what's implemented. But thinking about it
now, I see that this is quite wrong.)

The fact that it only works well with "je" suggests there's something wrong with the "jek tag bo" construction.

> It's odd however to have to read "li no pi'i mo'e ro namcu cu du li no"
> differently than "lo pilji be li no bei ro namcu cu du li no"

Is it? I don't know.

To analogise: I think the english pair
"zero times any number is equal to zero" and
"the product of zero and every number is equal to zero"
conveys the two meanings, using roughly the same structures.

But that's purely due to the different scopes of any/every, not to the variation between times/product-of. If you had "zero times every number is equal to zero" and "the product of zero and any number is equal to zero" you'd get the opposite result.

mu'o mi'e xorxes