**What is a structural
representation? Second version**

Initial posting: March 27,
2004.

Last updated: April 3, 2004 [several English typos, first paragraph in the abstract, penultimate paragraph on p. 6, and paragraph before Def. 11]

Complete paper (in PDF format)

**Abstract**

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 paradigms.

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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