It is easier to absorb the background of a researcher’s work from a coherent exposition than from many disjointed papers, so this book by Judea Pearl, a leading researcher in AI reasoning systems, makes a valuable contribution to this active field. Although Pearl says the book is based on his lecture notes, it is valuable as a report on current research and not as a balanced introduction to reasoning systems. A researcher active in a field usually cannot write a balanced textbook; Pearl develops competing approaches only far enough to demolish their bases. The bibliography is ample but obviously biased toward the author’s views, and the index seems adequate. A few misprints and questionable statements appear, but the author states his views and techniques clearly, and everybody trying to choose a conceptual framework for her or his AI programs should study this book.

The book is divided into three parts: chapters 1–3, 4–8, and 9 and 10. In the first two chapters Pearl establishes his approach; he concentrates on using Bayes’s formula to compute conditional probabilities for decision-making (rather than Bayes’s rule, which implies using uniform probabilities in case of ignorance). Unfortunately, he uses probabilities in de Finetti’s statistical sense instead of treating probability as an abstract basis of statistics. By disregarding absolute probabilities, he also omits some consequences of additional information. His terminology is not always clear--conditional probabilities are not really probabilities; rather, P ( X | Y ) is the weight of P ( Y ) in the computation of P ( X ) by partition. Also, Pearl’s theory would be more plausible if he had introduced sample spaces. This deficiency is especially unfortunate because Nilsson’s probabilistic logic, which is discussed briefly in chapter 9, can give a sound basis to all computations: it is universal, its consistency can be enforced by a simple set of inequalities [1], and it gives a framework for applying Dempster’s original theory for multiple inferences.

Chapter 3 deals with the graph-theoretical background for Markov and Bayesian networks and the use of such networks for computing conditional probabilities. In the last line of page 110, read “less” for “more.” The proof on page 115 is nonsensical, as it gives a probability of less than 1 as a product of terms greater than or equal to 1, although the theorem itself may be true.

Chapters 4 through 8 give the essence of Pearl’s probabilistic techniques under the titles “Belief Updating,” “Distributed Revision of Composite Beliefs,” “Decision and Control,” “Continuous Variables and Uncertain Probabilities,” and “Learning Structure from Data.” The author also discusses capturing the essence of induction, but science proceeds by induction only in the imagination of philosophers. In reality science uses statistics, not induction, and proceeds by insight into important paradigms. Given the coarse nature of guesses of probability values, order statistics might be the best tool for AI. (In defiance of common mathematical terminology, Pearl refers to vectors ( 1, . . . , 1) with the term “unit vector.”)

The last two chapters discuss a variety of topics under the headings of “Non-Bayesian Formalisms for Managing Uncertainty” and “Logic and Probability.” Pearl begins chapter 9 with a critical analysis of Dempster-Shafer theory. He cautions that “Dempster’s formula” is valid only for a single conclusion but does not emphasize this strongly enough.

Chapter 10 deals with default logic. The author first considers Reiter’s default logic. Then he follows up with some relevant proposals of his own in a detailed and positive discussion of Adams’s logic of conditionals. He could have avoided introducing the difficult ∀ ( x ) P ( A ( x ) | B ( x ) ) by using Keisler’s probability quantifiers [3]. Also, his exposition of Adams’s &egr;-logic is slightly marred by a failure to explicitly declare &egr; arbitrary (otherwise O ( &egr; ) makes no sense).