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]
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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