report: contin. symbol systems

[mclennan@cs.utk.edu]

    ** Please do not forward to other boards.  Thank you. **

The following technical report has been placed in the Neuroprose
archives at Ohio State.  Ftp instructions follow the abstract.
N.B.  The uncompressed file is long (1.82 MB), so you may have to
use the -s (symbolic link) option on lpr to print it.

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                    Continuous Symbol Systems
                   The Logic of Connectionism

                         Bruce MacLennan
                   Computer Science Department
                     University of Tennessee
                       Knoxville, TN 37996
                      maclennan at cs.utk.edu

                   Technical Report CS-91-145

                            ABSTRACT:

It has been long assumed that knowledge and thought are most
naturally represented as _discrete_symbol_systems_ (calculi).
Thus a major contribution of connectionism is that it provides an
alternative model of knowledge and cognition that avoids many of
the limitations of the traditional approach.  But what idea
serves for connectionism the same unifying role that the idea of
a calculus served for the traditional theories? We claim it is
the idea of a _continuous_symbol_system_.

This paper presents a preliminary formulation of continuous sym-
bol systems and indicates how they may aid the understanding and
development of connectionist theories.  It begins with a brief
phenomenological analysis of the discrete and continuous; the aim
of this analysis is to directly contrast the two kinds of symbols
systems and identify their distinguishing characteristics. Next,
based on the phenomenological analysis and on other observations
of existing continuous symbol systems and connectionist models, I
sketch a mathematical characterization of these systems.  Finally
the paper turns to some applications of the theory and to its
implications for knowledge representation and the theory of com-
putation in a connectionist context. Specific problems addressed
include decomposition of connectionist spaces, representation of
recursive structures, properties of connectionist categories, and
decidability in continuous formal systems.

A preliminary version of this paper was presented at the workshop
"Neural Networks for Knowledge Representation, Fourth Annual
Workshop of the Metroplex Institute for Neural Dynamics (MIND),"
Westlake TX, October 4-6, 1990.  Also presented at "ConnectFest
1990," sponsored by Indiana University Center for Research in
Concepts and Cognition, November 3-4, 1990.

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                        FTP INSTRUCTIONS

Either use "Getps maclennan.css.ps.Z", or do the following:

     unix> ftp archive.cis.ohio-state.edu (or 128.146.8.52)
     Name: anonymous
     Password: neuron
     ftp> cd pub/neuroprose
     ftp> binary
     ftp> get maclennan.css.ps.Z
     ftp> quit
     unix> uncompress maclennan.css.ps.Z
     unix> lpr -s maclennan.css.ps (or however you print postscript)

Note that the postscript version is missing three (nonessential)
figures that have been pasted into the hardcopy version.  If you
need hardcopy, then send your request to:

                       library at cs.utk.edu

     Bruce MacLennan
     Department of Computer Science
     107 Ayres Hall
     The University of Tennessee
     Knoxville, TN 37996-1301

     (615)974-0994/5067
     FAX: (615)974-4404
     maclennan at cs.utk.edu