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Readings in uncertain reasoning. (English) Zbl 0805.68121

San Mateo, CA: Morgan Kaufmann Publishers. x, 768 p. $ 41.50 /sc (1990).
The central topic of the book is how to deal with various degrees of uncertainty. Verbal indicators are, e.g., “perhaps”, “maybe”,“hardly”, “sure”, etc. The book is not a monography but a collection of “milestone” papers on uncertain reasoning. There are sections on “The meaning of probability” (chapter 2), “Decision making” (chapter 3), “Architectures and strategies for reasoning under uncertainty” (chapter 4), “Numerical uncertainty in expert systems” (chapter 5). “The Bayesian approach” (chapter 6), “Belief functions” (chapter 7), “Nonnumerical approaches to plausible inference” (chapter 8) and “Integrating probability and logic” (chapter 9). Each section contains an explanatory introduction by the leading researcher in his own field: Glenn Shafter (chapter 2, chapter 3, chapter 7, chapter 8), Paul R. Cohen (chapter 4) and Judea Pearl (chapter 5, chapter 6, chapter 8, chapter 9).
The book is biased toward the representation of uncertainty by probability. The reasons for that point of view are explicated in the introduction (chapter 1) and in the selected papers of the two following chapters. One is historic: probability theory is the earliest attempt to deal with uncertain empirical phenomena. In gambling the frequentist interpretation of probability is used for prognosis and evaluation. Gauss changed that point of view from probability as the frequency of actually replicated events with uncertain outcome to probability as the frequency of hypothetically replicatable events (measurements). The next theoretical progression was made by Bayes. He abandoned the frequentist interpretation of probability in favour of subjective or non-objective approach. Uncertainty is represented by subjective probabilities. The reason for the correctness of this interpretation is explained and proved by Savage by introducing utilities: if a person’s preferences are consistent, then his degree of uncertainty can be expressed by numbers that behave like probabilities. Those subjective probabilities could in principle be estimated empirically using the theoretical analysis of Savage. One of L. J. Savage’s papers is contained in chapter 2 [“The foundations of statistics reconsidered” (1961)]. Another paper [the first author, “Savage revisited”, Stat. Sci. 1, 463-501 (1986; Zbl 0613.62002)] elaborates this aspect further in chapter 3. The reader is convinced to use probabilities because they can be measured precisely (even in their subjective variant) and the formal apparatus is well developed.
Problems with the probabilistic approach are discussed in chapter 3 in two papers (Tversky & Kahneman, “Rational choice and the framing of decisions”, 1986; Shafer, “Savage revisited”, 1986). One of the problems rests in the imperfect discrimination of any human expert. The result of the empirical estimation procedure is not a subjective probability number but an estimated probability interval which cannot be divided any longer. That seems to be the reason why human subjects use imprecise linguistic attributes like “rather” etc. The second problem is partly due to imperfect discrimination and partly due to imperfect knowledge. So nontransitivity of estimates is the result and Savages analysis does not hold any longer. The third problem arises in the infeasability to extract a great number of consistent and valid subjective probability estimates. The fourth problem is the integration of preferences and beliefs of many different people.
Chapters after chapter 2 can be read in any order. Chapter 2 contains articles discussing the meaning of probability, the debate between frequentists and subjectivists, the debate about descriptive and normative aspects and the constructive nature of probability. Chapter 3 is concerned with the relation between probability and decision theory, its use by humans and its implementation in medicine. Chapter 4 is concerned with the role of system architecture, control of inference and conditional-independence structures. Chapter 5 contains pioneer articles on earlier implemented expert systems: MYCIN, PROSPECTOR, PIP, INTERNIST and CASNET. The last article is a about HUGIN a more recent Bayesian system. Chapters 6, 7, and 8 present competing theories for the explicit representation and handling of uncertainty. Chapter 9 tries an integration. A possible result can be the interpretation that qualitative relationships are abstractions from probability ideas and numerical probabilities are supplements to the classic symbolic systems.

MSC:

68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
68-06 Proceedings, conferences, collections, etc. pertaining to computer science
00B15 Collections of articles of miscellaneous specific interest

Citations:

Zbl 0613.62002
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