Mark.Derthick@G.CS.CMU.EDU (01/22/86)
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
hestenes@NPRDC.ARPA (Eric Hestenes) (01/28/86)
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 arpanet: hestenes@nprdc.ARPA other: ucbvax!sdcsvax!sdics!hestenes or hestenes@sdics.UUCP