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From: hestenes@NPRDC.ARPA (Eric Hestenes)
Newsgroups: mod.ai
Subject: Re: What is a symbol?
Message-ID: <8601272332.AA01413@sdics.CSL>
Date: Mon, 27-Jan-86 18:32:00 EST
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Posted: Mon Jan 27 18:32:00 1986
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Article 125 of net.ai:

In article <724@k.cs.cmu.edu>, dcp@k.cs.cmu.edu (David Plaut) writes:
> It seems there are three ways out of this dilemma:
> 
> 	(1) deny that connectionist systems are capable, in 
> 	    principle, of "true" general intelligent action;
> 	(2) reject the Physical Symbol System Hypothesis; or
> 	(3) refine our notion of a symbol to encompass the operation
> 	    and behavior of connectionist systems.
> 
> (1) seems difficult (but I suppose not impossible) to argue for, and since I
> don't think AI is quite ready to agree to (2), I'm hoping for help with (3)
> - Any suggestions? 	> David Plaut 	> (dcp@k.cs.cmu.edu)


Symbol is unfortunately an abused word in AI. Symbol can be used in several 
senses, and when you mix them things seem illogical, even though they are not.

Sense 1: A symbol is a token used to represent some aspect or element
	 of the real world.

Sense 2: A symbol is a chunk of knowledge / human memory that is of a certain
	 character. ( e.g. predicates, with whole word or phrase size units )

While PDP / connectionist models may not appear to involve symbolic processes,
meaning mental processes that operate on whole chunks of knowledge that
consistute symbols  they DO assign tokens as structures that represent some
aspect or element. For instance, if a vision program takes a set of
bits from a visual array as input, then at that point each of the bits are
assigned a symbol and then a computation is performed upon the symbol.
Given that pdp networks do have this primitive characterization in every
situation, they fit Newell's definition of a Physical Symbol System
[paraphrased as] "a broad class of systems capable of having and manipulating
symbols, yet realizable in the physical world." The key is to realize 
that while the information that is assigned to a token can vary quite
significantly, as in connectionist versus high level symbolic systems, 
the fact that a token has been assigned a value remains, and the manipulation
of that newly created symbol is carried out in either kind of system.

Many connectionists like to think of pdp systems as incorporating 
"microfeatures" or "sub-symbolic" knowledge. However, by this they do not mean
that their microfeatures are not symbols themselves. Rather they are actively
comparing themselves against traditional AI models that often insist on using
a single token for a whole schema ( word, idea, concept, production ) rather 
than for the underlying mental structures that might characterize a word.
A classical example is the ( now old ) natural language approach to thinking
that parses phrases into trees of symbols. Not even the natural language
people would contend that the contents of memory resembles that tree of
symbols in terms of storage. In this case the knowledge that is significant to
the program is encoded as a whole word. The connectionist might create a
system that parses the very same sentences, with the only difference being
how symbols are assigned and manipulated. In spite of their different
approach, the connectionist version is still a physical symbol system in the
sense of Newell. 

This point would be moot if one could create a connectionist machine that 
computed exactly the same function as the high-level machine, including 
manipulating high level symbols as whole. While both languages are Turing
equivalent, one has yet to see a system that can compile a high-level
programming language with a connectionist network. The problems with creating
such a machine are many; however, it is entirely possible, if not probable. 
See the paper for a Turing <--> Symbol System proof. 


Reference: Newell, Allen. Physical Symbol Systems. 
Cognitive Science 4, 135-183 (1980).

Copy me on replies.

Eric Hestenes
Institute for Cognitive Science, C-015
UC San Diego, La Jolla, CA 92093
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