Re: [ontolog-forum] What words mean

[paola.dimaio@xxxxxxxxx]

Thanks Azamat, John, Chris

I wonder if people have some examples of one root vs many roots trees to share
for study purposes

PDM

On Sat, Feb 23, 2008 at 4:03 PM, Azamat <abdoul@xxxxxxxxxxxxxx> wrote:

Paola,

By a strict definition, tree (diagram) is a plane figure that branches from a single root, what makes a graphic way to represent any hierarchical structure. Created as the mixed metaphors after family relationships (parent/child), graph theory (node), and botanic notions, the tree vocabulary is marked by the root nodes (superior, ancestor), internal nodes (parent/child), leaf nodes (child); subtrees and forest, a set of rooted trees. 

 

In a sense, trees are everywhere, whenever you deal with a hierarchical order:

1. in order theory and set theory, the tree structure makes a special kind of partial order;

2. in graph theory, it makes a connected acyclic graph, undirected or directed;

3. in knowledge representation, it reflects all taxonomic knowledge;

4. in family, it represents phylogenetic family trees, cladograms;

5. in society, any hierarchical social structure;

6. in linguistics, syntactic phrasal structure as S > NP VP;

7. in library science, Dewey Decimal System;

8. in internet and Telecommunications, root nodes servers, domain servers, etc;

9. in web, Yahoo subject index, OPD, the arrangement of web pages in a web site

10. in computing, tree data structure.

 

regards,

azamat abdoullaev

 

 

 

 

----- Original Message -----

From: paola.dimaio@xxxxxxxxx

To: [ontolog-forum]

Sent: Friday, February 22, 2008 8:23 PM

Subject: Re: [ontolog-forum] What words mean

Christopher and all

is there a rule or other guideline to prescribe when a tree should have one, and when more than one root?

thanks
PDM

On Sat, Feb 23, 2008 at 1:19 AM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:

On Feb 21, 2008, at 1:00 AM, John F. Sowa wrote:
> Dear Matthew, Pat, Chris, and Ed,
>
> Since other people have responded very well, I'd just like to
> comment on one point:
>
> CM> ... in fact, you can define a tree to be a connected acyclic
> graph.
>

> That is only true for undirected trees ...

Quite right, I accessed the wrong memory address there. :-)  For
directed trees (which were the only kind that made sense in the
context) one has to include the unique immediate predecessor condition
Pat mentioned.  The more formal definition in set theory is that a
tree is a partially ordered set (T,<) such that set of the
predecessors of any given node is well-ordered by <.  This definition
permits trees to have more than one root, but that could of course be
ruled out by a further condition.

Intuitively, the idea is that, in a tree (with a single root), there
is a unique, discrete path from the root node to any other node in the
tree.  (This of course entails the unique immediate predecessor
condition.)

-chris

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