[Top] [All Lists]

Re: [ontolog-forum] What words mean

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Fri, 22 Feb 2008 12:19:44 -0600
Message-id: <80319939-1BDF-46A8-8928-C7F885245D66@xxxxxxxx>
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 ...    (01)

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.    (02)

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.)    (03)

-chris    (04)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (05)

<Prev in Thread] Current Thread [Next in Thread>