On Fri, 19 Oct 2001, Yves Kodratoff wrote:
> People in Machine Learning have been asking themselves since ever how to use
> and how to built structures.
>
> People in Knowledge Acquisition build "ontologies" that are structures.
> ........................................................................
> Is a structural representation a set of theorems? (of the form ForAll x,
> subclass (x) implies Class (x), as dog(x) implies mammal(x))? Is not a kind
> of heritance property within the structure necessary?
>
> If you answer no, then what is a structural representation, as opposed to a
> non structural one?
>
> In this discussion devoted only to ETS? (sorry, I do not know this formalism)
Yves,
Although this discussion is supposed to be devoted to ETS, I would like to
answer very briefly you questions (sorry, this week I'm completing a
very long grant application).
The answer to your question, of course, can be found in the paper under
discussion. To simplify, beautifully enough, it appears that the key to
structural representation is a "satisfactory" model for inductive class
representation: in case of the ETS model, the formalism for the
(inductive) class representation pointed the way to a hopefully proper
treatment of the "structural" object representation via a far-reaching
generalization of the classical (and very basic) Peano construction of
natural numbers. Again, generalizing the "logic" of Peano construction,
our treatment was guided by the concept of a structural operation (we
called it a "transformation") acting on an object and thus leading to the
construction of new objects.
Since now, in contrast to natural numbers, the participating operations
are not identical (and their number is not bounded), the structural
representation must includes now the actual constructive "history", i.e.
the sequence of transformations, that led to the object's
construction/formation.
Again, sorry for the condensed answer (see also my home page).
-- Lev
***************************************************************************
Lev Goldfarb Tel: 506-458-7271
Faculty of Computer Science Tel(secret.): 453-4566
University of New Brunswick Fax: 506-453-3566
P.O. Box 4400 E-mail: [EMAIL PROTECTED]
Fredericton, N.B., E3B 5A3 Home tel: 506-455-4323
Canada
http://www.cs.unb.ca/profs/goldfarb/goldfarb.htm
