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Paperback | $65.00 X | £54.95 | 504 pp. | 7 x 9 in | 18 b&w illus. | April 2017 | ISBN: 9780262533805
eBook | $46.00 X | March 2017 | ISBN: 9780262340489
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Reasoning about Uncertainty, Second Edition


In order to deal with uncertainty intelligently, we need to be able to represent it and reason about it. In this book, Joseph Halpern examines formal ways of representing uncertainty and considers various logics for reasoning about it. While the ideas presented are formalized in terms of definitions and theorems, the emphasis is on the philosophy of representing and reasoning about uncertainty. Halpern surveys possible formal systems for representing uncertainty, including probability measures, possibility measures, and plausibility measures; considers the updating of beliefs based on changing information and the relation to Bayes’ theorem; and discusses qualitative, quantitative, and plausibilistic Bayesian networks.

This second edition has been updated to reflect Halpern’s recent research. New material includes a consideration of weighted probability measures and how they can be used in decision making; analyses of the Doomsday argument and the Sleeping Beauty problem; modeling games with imperfect recall using the runs-and-systems approach; a discussion of complexity-theoretic considerations; the application of first-order conditional logic to security.

Reasoning about Uncertainty is accessible and relevant to researchers and students in many fields, including computer science, artificial intelligence, economics (particularly game theory), mathematics, philosophy, and statistics.

About the Author

Joseph Y. Halpern is Professor of Computer Science at Cornell University. He is the author of Actual Causality and the coauthor of Reasoning about Knowledge, both published by the MIT Press.


Halpern presents a masterful, complete, and unified account of the many ways in which the connections between logic, probability theory, and commonsensical linguistic terms can be formalized. Terms such as ‘true,’ ‘certain,’ ‘plausible,’ ‘possible,’ ‘believed,’ ‘known,’ ‘default,’ ‘relevant,’ ‘independent,’ and ‘preferred’ are given rigorous semantical and syntactical analyses, and their interrelationships explicated and exemplified. An authoritative panoramic reference for philosophers, cognitive scientists, and artificial intelligence researchers.
Judea Pearl, Computer Science Department, University of California, Los Angeles

For some years now I have been testing a hypothesis: if a topic involving probability is of current interest to a philosopher, then Joseph Halpern has proved an important result that is relevant to it. Its accuracy can be gauged by the frequency with which I recommend his papers to colleagues and students. This book, which presents all these valuable contributions in a single volume, provides a rich source of technical and philosophical insight.
Bas C. van Fraassen, Department of Philosophy, Princeton University

Reasoning about Uncertainty pursues its own unified theoretical perspective in a remarkably systematic way, yet it is also a remarkably rich and complete textbook. It will be a rewarding book to work through for students and researchers alike.”
Wolfgang Spohn, Department of Philosophy, University of Konstanz