Fwd: What is a structural represetation?

Header field too long (>1024) ---- Date: Thu, 28 Jun 2001 02:41:22 -0300 (ADT) From: Lev Goldfarb <goldfarb(a)unb.ca> To: ai(a)cs.stanford.edu, ai-stats(a)watstat.uwaterloo.ca, ail-l(a)austin.onu.edu, allstat(a)jiscmail.ac.uk, annimab(a)listserv.hum.gu.se, arpanet-bboards(a)edu.mit.lcs.mc, bayes-news(a)stat.cmu.edu, biocomp(a)umiacs.umd.edu, cogpsy(a)phil.uu.nl, colt(a)cs.uiuc.edu, community(a)mlnet.org, connectionists(a)cs.cmu.edu, dalist(a)fuqua.duke.edu, datamine-l(a)nautilus-sys.com, dbworld(a)cs.wisc.edu, editor(a)kdnuggets.com, empiricists(a)csli.stanford.edu, fuzzy-mail(a)dbai.tuwien.ac.at, ga-list(a)aic.nrl.navy.mil, gann-list(a)cs.cmu.edu, genetic-programming(a)cs.stanford.edu, hybrid-list(a)cs.ua.edu, idss(a)socs.uts.edu.au, ie-list(a)cs.ucl.ac.uk, inductive(a)unb.ca, kdd(a)gte.com, machine-learning(a)egroups.com, ml(a)ics.uci.edu, neuron(a)cattell.psych.upenn.edu, neuron(a)hpl.hp.com, news-announce-conferences(a)uunet.uu.net, nl-kr(a)cs.rpi.edu, planning(a)asu.edu, reinforce(a)cs.uwa.edu.au, sigart(a)vaxa.isi.edu, simulation(a)ufl.edu, uai(a)cs.orst.edu, ai-medicine(a)smi.stanford.edu Subject: What is a structural represetation? (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(a)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(a)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.