DON@atc.bendix.COM.UUCP (07/08/87)
>From: Jenny <ISCLIMEL%NUSVM.BITNET@wiscvm.wisc.edu> >Subject: so what about plausible reasoning ? >As I read articles on plausible reasoning in expert systems, I come to the >conclusion that experts themselves do not exactly work with numbers as they >solve problems. You are correct in several senses. One, the psychology literature has shown time and time again that human belief revision does not conform to Bayesian evidence accumulation (e.g., Edwards, 1968; Fischhoff & Beyth-Marom, 1983; Robinson & Hastie, 1985; Schum, Du Charme, & DePitts, 1973; Slovic & Lichtenstein, 1971). Two, it does not appear that humans literally use any of the methods. However, the humans do appear to be weighing alternatives. Although, for a period, it may seem that the humans are performing sequential hypothesis testing, for stochastic domains with non-trivial uncertainty, humans gather support for a large set of hypotheses at the same time. They may appear to only gather support for their "favorite"; however, if asked for an ordering over the alternatives or if asked how much they believe the alternatives, it is obvious that they have allowed the evidence to change their beliefs about the non-favorite hypotheses (e.g., Robinson & Hastie, 1985). The question becomes, "what are they doing?" For the sake of argument, let's take your assertion and say they are not explicitly manipulating numbers -- it does seem absurd that the automobile mechanic who can't add simple integers without a calculator could possibly perform the complex aggregations necessary to use numbers. Another possibility is that they are performing a type of non-monotonic logic with the choice of assumptions and generation and testing of possible worlds. This possibility suggests that, if the human is not using numbers at any level, the human's choice of one assumption over another uses a simple set of context sensitive rules. The only time the human should change assumptions (generate an alternative path or possible world) is if the current assumptions are defeated or if some magical attentional process causes the human to arbitrarily try another path. When choosing another path, there should be a fixed set of rules guiding the choice of alternative -- there can be no idea of "this looks a little stronger than that" because such comparisons require a comparison metric which is not built into non-monotonic logics. The psychological research on human search strategies (especially for games such as chess) suggests that humans often abandon one search path to test another which looks like it might be as strong or stronger and then return to the original path. This return to the original path leads to a rejection of the hypothesis that humans maintain a set of assumptions until evidence refutes those assumptions. By my previous argument, then, if non-monotonic logics model human decision making, the humans must be choosing to change path generation based on an attentional mechanism. If numbers are not involved, then the attentional mechanism is probably rule-driven. Of course, I've laid out a straw man. I've said it's either numbers or rules; however, there are probably many other possibilities. The most likely possibility is an analog process something akin to comparisons of weights. If we were to model this process in a computer, we would use numbers; so, we're back to numbers. The trouble with just using numbers, of course, is determining how to combine them under different circumstances and how to interpret them. Plausibility reasoning has been used because it, at least, suggests methods for both of these processes. Something, even an approximation, which has validity at some level, is better than nothing. Rather than turn this into a thesis, let's go on to your next point. >And many of them are not willing to commit themselves into >specifying a figure to signify their belief in a rule. Hum, this sounds like something from Buchanan and Shortliffe. Let's think about the implications of this argument. You're saying, if humans find it difficult to generate numbers to represent their degrees of belief, then numbers must be ineffective. Perhaps even at a higher-level, if humans find some piece of knowledge or knowledge artifact difficult to specify, then it probably is ineffective. What evidence do we have for these claims? What are the implications of these claims? From a personal standpoint, I find any knowledge, beyond the trivial, is difficult to specify in some external formalism (including writing, rules, and probabilities). It seems unlikely that we will ever generate external formalisms which allow painless knowledge transfer. Does that imply that knowledge transfer is hopeless? Let's hope not because that is the modus operandi of the human species. Granted, it will not be perfect, it will be painfull, it will take time, but does that imply that it is worthless? We "know" that human experts have knowledge which is effective. There is growing evidence that purely logical formalisms for representing this knowledge will not work for all problem domains due to the stochastic nature of the domains or the incomplete understanding of the domain. Does this mean that automated problem solving must be limited to non-stochastic domains in which there is a full and complete understanding of the causal relations and elements? I fear that I have left the primary argument which I wanted to use in response to your statement. I looked at statements such as these and asked myself whether "comfort" was a legitimate metric for determining the effectiveness of knowledge. This question suggested an experiment in which different sets of experts were asked to generate the comfortable MYCIN confidence factors, the uncomfortable but definable conditional and a priori probabilities needed for Bayes' theorem, and the interesting, but perhaps not well-defined, probability bounds for the typical Dempster-Shafer formulation. I ran this experiment in which the experts were matched for knowledge in the domain. Each expert was asked to provide the parameters needed for only one of the plausibility reasoning formulisms. The results were that, at a superficial level, humans can provide better MYCIN and Dempster-Shafer parameters than Bayesian numbers. However, when considering how these numbers are used and how errors in the numbers propagate through repeated applications of the aggregation formulae, the Bayesian parameters led to more effective automated decision making than the MYCIN parameters. The performance of the Demspter-Shafer parameters was not significantly better or worse than either system in this test. (This research is documented in two papers -- ask me for references.) The conclusion: the domain expert's comfort is not a legitimate determinant of knowledge effectiveness. >If one obtains two conclusions with numbers indicating some significance, >say 75 % and 80 %, can one say that the conclusion with 80% significance is >the correct conclusion and ignore the other one ? There is a fundamental problem here. If you are refering to percentages, then the numbers cannot add to more than 100. You are correct in that a decision theory for plausibility reasoning must take into account the accuracy of the parameters, and I believe that some researchers have not considered this problem; however, most plausibility reasoning researchers consider the decision theory to be an important component which must be given strict attention. >These numbers do not seem to mean much since they are just beliefs or >probabilties. I alluded to this problem earlier. Actually, if they are probabilities, they mean a lot. Probabilities have clear operational and theoretical definitions. Some, for example Shafer (1981), have suggested that the definition of probabilities can be extended to better account for the subjective nature of the probabilities used in most decision support systems. The real problem is with the MYCIN style confidence factors. Although Heckman (1986) has developed a formal interpretation of confidence factors, the interpretation is ad hoc and it seems difficult to imagine that domain experts use this interpretation. The meaningfulness of the numbers is an important criterion for determining the successful application of the numbers and is one of the strongest arguments for using probabilities and perhaps for using Bayes' theorem. Donald H. Mitchell Don@atc.bendix.com Bendix Aero. Tech. Ctr. Don%atc.bendix.com@relay.cs.net 9140 Old Annapolis Rd. (301)964-4156 Columbia, MD 21045