Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.3 4.3bsd-beta 6/6/85; site ucbvax.BERKELEY.EDU Path: utzoo!decvax!decwrl!ucbvax!ailist From: Mark.Derthick@G.CS.CMU.EDU Newsgroups: mod.ai Subject: Re: What is a Symbol? Message-ID: <8601300518.AA05105@ucbvax.berkeley.edu> Date: Wed, 22-Jan-86 14:41:45 EST Article-I.D.: ucbvax.8601300518.AA05105 Posted: Wed Jan 22 14:41:45 1986 Date-Received: Fri, 31-Jan-86 02:18:03 EST Sender: daemon@ucbvax.BERKELEY.EDU Organization: The ARPA Internet Lines: 81 Approved: ailist@sri-ai.arpa This is a response to David Plaut's post (V4 #9) in which he maintains that connectionist systems can exhibit intelligent behavior and don't use symbols. He suggests that either he is wrong about one of these two points, or that the Physical Symbol System Hypothesis is wrong, and seeks a good definition of 'symbol. First, taking the PSSH seriously as subject to empirical confirmation requires that there be a precise definition of symbol. That is, symbol is not an undefined primitive for Cognitive Science, as point is for geometry. I claim no one has provided an adequate definition. Below is an admittedly inadequate attempt, together with particular examples for which the definition breaks down. 1) It seems that a symbol is foremost a formal entity. It is atomic, and owes its meaning to formal relationships it bears to other symbols. Any internal structure a [physical] symbol might posess is not relevant to its meaning. The only structures a symbol processor processes are symbol structures. 2) The processing of symbols requires an interpreter. The link between the physical symbols and their physical interrelationships on the one hand, and their meaning on the other, is provided by the interpreter. 3) Typically, a symbol processor can store a symbol in many physically distinct locations, and can make multiple copies of a symbol. For instance, in a Lisp blocks world program, many symbols for blocks will have copies of the symbol for table on their property lists. Many functionally identical memory locations are being used to store the symbols, and each copy is identical in the sense that it is physically the same bit pattern. I can't pin down what about the ability to copy symbols arbitrarily is necessary, but I think something important lurks here. The alternative to symbolic representations, analog (or direct) representations, do not lend themselves to copying so easily. For instance, on a map, distance relations between cities are encoded as distances between circles on paper. Many relations are represented, as in the case with the blocks world, but you can't make a copy of the circle representing a city. If it's not in the right place, it just won't represent that city. 4) Symbols are discrete. This point is where connectionist representations seem to diverge most from prototypical symbols. For instance, in Dave Touretzky's connectionist production system model (IJCAI 85), working memory elements are represented by patterns of activity over units. A particular element is judged to be present if a sufficiently large subset of the units representing the pattern for that element are on. Although he uses this thresholding technique to enable discrete answers to be given to the user, what is going on inside the machine is a continuum. One can take the pattern for (goal clear block1) and make a sequence of very fine grained changes until it becomes the pattern for (goal held block2). To show where my definition breaks down, consider numbers as represented in Lisp. I don't think they are symbols, but I'm not sure. First, functions such as ash and bit-test are highly representation dependent. Everybody knows that computers use two's complement binary representation for arithmetic. If they didn't, but used cons cells to build up numbers from set theory for instance, it would take all day to compute 3 ** 5. Computers really really have special purpose hardware to do arithmetic, and computer programmers, at least sometimes, think in terms of ALU's, not number theory, when they program. So the Lisp object 14 isn'sometimes t atomic, sometimes its really 1110. Its easy to see that the above argument is trying to expose numbers as existing at a lower level than real Lisp symbols. At the digital logic level, then, bits would be symbols, and the interpreter would be the adders and gates that implement the semantics of arithmetic. Similarly, it may be the case that connectionist system use symbols, but that they do not correspond to, eg working memory elements, but to some lower level object. So a definition of "symbol" must be relative to a point of view. With this in mind, it seems that confirmation of the Physical Symbol System Hypothesis turns on whether an intelligent agent must be a symbol processor, viewed from the knowledge level. If knowledge level concepts are represented as structured objects, and only indirectly as symbols at some lower level, I would take it as disconfirmation of the hypothesis. I welcome refinements to the above definition, and comments on whether Lisp numbers are symbols, or whether ALU bits are symbols. Mark Derthick mad@g.cs.cmu.edu