Paper "What is a structural representation?"

Lev Goldfarb goldfarb at
Tue Mar 30 03:12:48 EST 2004

(My apologies if you receive several copies of this message)

Dear colleagues,

It is my great pleasure to inform you of the second, SUBSTANTIALLY modified, 
version of our earlier (2000) paper on structural representation. 
You will find the second version at


The paper's abstract is appended below.

This paper is absolutely unique, in the sense that it still remains the only one
addressing the issue of structural representation at a fundamental level--as it
deserves to be treated--which is why it should be of interest to many researchers
in various areas.  Moreover, the concept of structural representation emerging from 
the formalism outlined in this paper has nothing to do with the conventional one: a
structural representation must capture the corresponding "generative history".  

We would GREATLY appreciate any comments regarding this paper. 

(We also intend to discuss the paper on the INDUCTIVE mailing list.  To subscribe, send
the following text



Best regards,

Lev Goldfarb

Faculty of Computer Science 
University of New Brunswick 
540 Windsor Street 
Fredericton, N.B., E3B 5A3 


                          What is a structural representation?
                                       Second version

               Lev Goldfarb, David Gay, Oleg Golubitsky, Dmitry Korkin
                              Faculty of Computer Science
                                      UNB, Fredericton


We outline a formalism for "structural", or "symbolic", representation, the necessity
of which is acutely felt in all sciences.  One can develop an initial intuitive
understanding of the proposed representation by simply generalizing the process of
construction of natural numbers: replace the identical structureless units out of which
numbers are built by several structural ones, attached consecutively.  Now, however,
the resulting constructions embody the corresponding formative/generative histories,
since we can see what was attached and when.

The concept of class representation--which inspired and directed the
development of this formalism--differs radically from the known concepts of class.
Indeed, the evolving transformation system (ETS) formalism proposed here is the first
one developed to support that concept; a class representation is a finite set of
weighted and interrelated transformations ("structural segments"), out of which class
elements are built.

The formalism allows for a very natural introduction of representational levels: a
next-level unit corresponds to a class representation at the previous level.

We introduce the concept of "intelligent process", which provides a suitable scientific
environment for the investigation of structural representation.  This process is
responsible for the actual construction of levels and of representations at those
levels; conventional "learning" and "recognition" processes are integrated into this
process, which operates in an unsupervised mode.  Together with the concept of
structural representation, this leads to the delineation of a new field--inductive
informatics--which is intended as a rival to conventional information processing

>From the point of view of the ETS formalism, classical discrete "representations"
(strings, graphs) now appear as incomplete special cases at best, the proper
"completion" of which should incorporate corresponding generative histories (e.g. those
of strings or graphs).


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