Halpern’s first edition, published in 2003, was recognized as: “a fine book and a mighty piece of scholarship” [1]; “an inspiring book, multifaceted and full of fresh reflections, findings and examples” [2]; and “a unified introduction to a certain philosophy for representing and reasoning about uncertainty” [3]. One reviewer observed that “there can be very few researchers interested in uncertain reasoning who would not find much of value in this work” [4].

As the author notes, much has happened in the world of uncertain reasoning since 2003, but as with the first edition, this book focuses mainly on work relating to Halpern’s own research (with ten additional papers by Halpern in the bibliography) and does not attempt the (impossible) task of offering comprehensive coverage of this major field. This second edition includes some new topics--for example, a discussion of complexity theoretic considerations, and new approaches to security protocols--but overall is a modest updating of the first edition. This does not detract from the book’s importance to the field.

The book contains 12 chapters and an extensive bibliography of over 400 works. There are many examples, and each chapter concludes with a set of exercises. The first five chapters introduce different approaches to representing information (for example, probability theory, belief functions, possibility measures) and how to update that information when new, relevant information is available. The unifying theme is the notion of plausibility measure. The later chapters provide a selection of techniques for which reasoning about uncertainty is core, including multiagent systems; logic and probability; default and counterfactual reasoning; and belief revision. The concluding chapters offer synthesis and overall remarks.

The book stands as a substantive and essentially self-contained study of formalisms for representing uncertainty and their mathematical relationships, and is not an endorsement for any particular perspective. The target audience is unchanged: graduate students and researchers in disciplines such as artificial intelligence (AI), economics, mathematics, and statistics. The book is highly recommended both as a textbook for a graduate course and as a reference for graduate students and researchers in areas related to artificial intelligence and statistics.

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