What is a structural represetation?

From: Lev Goldfarb (goldfarb@unb.ca)
Date: Fri Jun 29 2001 - 19:14:36 MET DST

  • Next message: S. F. Thomas: "Elkan and the core problem of generalized connectives"

    (Our apologies if you receive multiple copies of this announcement)

    Dear colleagues,

    The following paper, titled "What is a structural representation?",

                         ( http://www.cs.unb.ca/profs/goldfarb/struct.ps )

    which we believe to be, in a sense, the first one formally addressing the
    issue of structural representation and proposing the formal ETS model,
    should be of interest to many researchers in various areas.

    It implies, in particular, that the properly understood (non-trivial)
    "structural" representations cannot be "replaced" by the classical
    numeric, e.g. vector-space-based, representations. Moreover, the concept
    of "structural" representation emerging from the ETS model is not the one
    familiar to all of you.
     
    (The abstract of the paper is appended below; for a change, the default
    paper size is A4. Unfortunately for some, the language of the paper is of
    necessity quite formal, since the main concepts do not have any analogues
    and therefore must be treated carefully.)

    Although the proposed model was motivated by, and will be applied to, the
    "real" problems coming from such areas as pattern recognition, machine
    learning, data mining, cheminformatics, bioinformatics, and many others,
    in view of the required radical rethinking that must now go into its
    implementations, at this time, we can only offer a very preliminary
    discussion, in the following companion paper, addressing the model's
    potential applications in chemistry
     
                          http://www.cs.unb.ca/profs/goldfarb/cadd.ps

    (please keep in mind that the last paper was written on the basis of an
    earlier draft of the paper we are announcing now and it will be updated
    accordingly next month).

    We intend to discuss the paper shortly on INDUCTIVE mailing list.

    (To subscribe, send to INDUCTIVE-SERVER@UNB.CA the following text
        SUBSCRIBE INDUCTIVE FIRSTNAME LASTNAME)

    We would greatly appreciate any comments regarding both of the above
    papers.

    Best regards,

         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: goldfarb@unb.ca
         Fredericton, N.B., E3B 5A3 Home tel: 506-455-4323
         Canada
     
     
         http://www.cs.unb.ca/profs/goldfarb/goldfarb.htm

    *****************************************************************************

                         WHAT IS A STRUCTURAL REPRESENTATION?

                    Lev Goldfarb, Oleg Golubitsky, Dmitry Korkin

                             Faculty of Computer Science
                             University of New Brunswick
                               Fredericton, NB, Canada

      We outline a formal foundation for a "structural" (or "symbolic")
    object/event representation, the necessity of which is acutely felt in
    all sciences, including mathematics and computer science. The proposed
    foundation incorporates two hypotheses:
        1) the object's formative history must be an integral part of the
           object representation and
        2) the process of object construction is irreversible, i.e. the
           "trajectory" of the object's formative evolution does not intersect
           itself.
    The last hypothesis is equivalent to the generalized axiom of (structural)
    induction. Some of the main difficulties associated with the transition
    from the classical numeric to the structural representations appear to be
    related precisely to the development of a formal framework satisfying
    these two hypotheses. The concept of (inductive) class--which has inspired
    the development of this approach to structural representation--differs
    fundamentally from the known concepts of class.
      In the proposed, evolving transformations system (ETS), model, the class
    is defined by the transformation system---a finite set of weighted
    transformations acting on the class progenitor--and the generation of the
    class elements is associated with the corresponding generative process
    which also induces the class typicality measure.
      Moreover, in the ETS model, a fundamental role of the object's class in
    the object's representation is clarified: the representation of an object
    must include the class.
      From the point of view of ETS model, the classical discrete
    representations, e.g. strings and graphs, appear now as incomplete
    special cases, the proper completion of which should incorporate the
    corresponding formative histories, i.e. those of the corresponding strings
    or graphs.

    ############################################################################
    This message was posted through the fuzzy mailing list.
    (1) To subscribe to this mailing list, send a message body of
    "SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at
    (2) To unsubscribe from this mailing list, send a message body of
    "UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com"
    to listproc@dbai.tuwien.ac.at
    (3) To reach the human who maintains the list, send mail to
    fuzzy-owner@dbai.tuwien.ac.at
    (4) WWW access and other information on Fuzzy Sets and Logic see
    http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info
    (5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html



    This archive was generated by hypermail 2b30 : Fri Jun 29 2001 - 19:30:09 MET DST