On 2012/09/29 10:10, Arnaud F. wrote:
> Le samedi 29 septembre 2012 04:18:43 UTC+2, DKleinecke a écrit :
>> On Sep 27, 11:57 pm, "Arnaud F." <
fournet.arn...@wanadoo.fr> wrote:
>
>>
>>> What does "hierarchy" describe?
>>
>>
>>
>> Actually I have been guessing what they meant. It is not, so far as I
>>
>> know, a standard technical term. But hierarchy is used often these
>>
>> days to describe what are also called trees. For example XML.
> ***
>
> yes, but there are several kinds of trees,
>
> for example, if we take "I go home"
>
> trees or stemmas à la Tesnière look like:
> go [top of hierarchy]
> " "
> " "
> I home
>
> Which describes how words like I and home depends on the predicate = to go
>
> This is not the same kind of "trees", as using GN GV and all the rest.
You might look at the ASTs (Abstract Syntax or Semantic Tree) used when
constructing compilers:
https://en.wikipedia.org/wiki/Abstract_syntax_tree
The math name for this kind of trees one gets, also when using nested
parenthesizes, is a finite directed and ordered tree. "Directed" means
that the edges are arrows, which is top down in your diagram above, and
"ordered" means that there is a total ordering among the edges of each
node, which is left-to-right above.
Using the notation similar to that of the paper, I might use say prefix
notation f(x_1, ..., x_k) to write a node f with a sequence of edges
x_1, ..., x_k. Then the diagram above becomes "go"("I", "home").
The next question is whether it is useful for describing natural
languages, where the order might shift. It might be better to use
labels. For example, "go"{A: "I", B: "home"}, so that this is the same
as "go"{B: "home", A: "I"}, that is, the order can be shifted - this is
why I sneaked in "{...}" instead of "(...)", looking more like sets or
data structures in C. This is used in some computer languages too, but
from the formal point of view, one just have another data type usually
called a "associative array".
https://en.wikipedia.org/wiki/Associative_array
Hans