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A Model of Inexact Reasoning in Medicine

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Reprinted in Readings in Uncertain Reasoning, G. Shafer and J. Pearl, eds., pp. 259-273, San Mateo, CA: Morgan Kaufmann Publishers, Inc., 1990.See also: Stanford Center for Biomedical Informatics Research (BMIR).… quantifying confirmation and then manipulating the numbers as though they were probabilities quickly leads to apparent inconsistencies or paradoxes. Carl Hempel presented an early analysis of confirmation (Hempel, 1965), pointing out as we have that C[h,e] is a very different concept from P(hle ). His famous Paradox of the Ravens was presented early in his discussion of the logic of confirmation. Let hl be the statement that "all ravens are black" and h2 the statement that "all nonblack things are nonravens." Clearly hi is logically equivalent to h,2. If one were to draw an analogy with conditional probability, it might at first seem valid, therefore, to assert that C[hl,e] = C[h2,e] for all e. However, it appears counterintuitive to state that the observation of a green vase supports hi, even though the observation does seem to support h,2. C[h,e] is therefore different from P(hle) for it seems somehow wrong that an observation of a vase could logically support an assertion about ravens. Another characteristic of a quantitative approach to confirmation that distinguishes the concept from probability was well-recognized by Carnap (1950) and discussed by Barker (1957) and Harrd (1970). They note it is counterintuitive to suggest that the confirmation of the negation of a hypothesis is equal to one minus the confirmation of the hypothesis, i.e., C[h,e] is not 1 - C[-qh,e]. The streptococcal decision rule asserted that a gram-positive coccus growing in chains is a Streptococcus with a measure of support specified as 7 out of 10. This translates to C[h,e]=0.7 where h is "the organism is a Streptococcus" and e is the information that "the organism is a gram-positive coccus growing in chains." As discussed above, an expert does not necessarily believe that C[mh,e] = 0.3. The evidence is said to be supportive of the contention that the organism is a Streptococcus and can therefore hardly also support the contention that the organism is not a Streptococcus. Ch.13 of Mycin Book; revised from Math. Biosci. 23:351-379


Computer-based consultations in clinical therapeutics: Explanation and rule-acquisition capabilities of the MYCIN system

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Reprinted in Sheehy, N. and Capman, A.J., eds. The International Library of Critical Writings in Psychology: Cognitive Science, London: Edward Elgar Publishing Ltd., pp. 250-267, 1995.See also: Stanford HPP 75-2.Computers and Biomedical Research, 8 (4): 303-320.



Dimensions of Representation

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"Workers in cognitive science have worried about what people know, and how to represent such knowledge within a theory. Psychologists such as Paivio (1974) and Pylyshyn (1973) have argued, for example, over two alternative forms for visual memory in humans. The style of their arguments, which we return to at the end of this chapter, is to set up opposing characterizations and to argue about which one has more "natural" properties with respect to observed phenomena.I claim that a more appropriate way of discussing the issues involved is to characterize each representation in terms of how it answers certain questions posed in this chapter. I pose these questions in terms of a set of design issues one would face in designing or analyzing an understander system--a system (human or computer) which could use the knowledge to achieve some goal. I propose a framework for viewing the problems of representation. In this framework each of the design issues defines a dimension of representation--a relatively independent way of looking at representations.In this chapter I emphasize the structure of alternative solutions to the design issues. I illustrate the design options through three specific representations described here, and in examples from the literature and other chapters in this book. By considering representations along the separate dimensions, it often becomes apparent that a pair of seemingly disparate representations differ in very few significant features."in Representation and Understanding. Eds. D.G. Bobrow and Allan Collins. New York: Academic Press, 1975., pp. 1-34.