On Mon, Aug 20, 2012 at 3:08 PM, Jorge Llambías
<jjllambias@hidden.email> wrote:
For example, starting with ((t1 t2)(t3 t4)):
/\
/ \
/ \
/\ /\
t1 t2 t3 t4
t3
/ \
t1 t4
\
t2
o Voilà, we're done.
If I start with (((t1 t2) t3) t4) instead:
/\
/ \
/\ \
/ \ \
/\ \ \
t1 t2 t3 t4
I seem to end up with the same raised tree you ended up with:
I first raise t1:
/\
/ \
/\ \
t1 \ \
\ \ \
t2 t3 t4
then t3 (since t1 already has a right branch):
/\
t3 \
/ \
t1 \
\ \
t2 t4
And t3 again:
t3
/ \
t1 \
\ \
t2 \
\
t4
If two different trees end up having the same raised tree, then encoding the raised tree won't be enough to encode any tree.
I was sloppy on giving all the constraints on raising, because I have not worked out every permutation towards a generalization of the scheme (nor likely will I). But one thing that seems necessary is that in the final production, there is going to be some precedence hierarchy among terminal tones. There are several possible precedence hierarchies, but in all variations, head raising has to be disallowed if it violates a precedence rule.
In your example, when t3 was raised over t1, it seemed to indicate that a right branch (t1\t2) takes precedence over a left branch (t2/t3), because what you had so far was t1(è) t2(ě) t3(é) and that can be parsed two different ways, but only one way matches the tree. Then you raised t3 over t4, which seemed to indicate the opposite. The only way to salvage your example is by specifying that a double-branching (falling-tone) terminal groups with its left child first, but a right-branching (low tone) terminal takes precedence over a falling tone. That's certainly an allowable variation, but it's not what I had in mind with my example.
By the way, to be honest, I am not 100% sure that any variation of this system is generalizable over all possible trees as opposed to a specific syntax as in my simplified Lojban example, but I do know that given a string of N terminals, the number of possible binary groupings is the (N - 1)th catalan number, and and the number of possible raised trees is the Nth Catalan number, which seems to give some elbow room. So maybe it's possible, but I don't really know.