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Reasoning about Uncertainty Paperback – August 12, 2005

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Editorial Reviews


For more than a decade, the study of uncertain reasoning has been graced
by the breadth, openness, and agility of Joe Halpern's intellect. More than any of
his colleagues, Joe has sought to reconcile and unify the diverse insights and
methods for reasoning about knowledge and uncertainty that have been developed and
championed in various academic fields. This cheerful, measured, and comprehensive
book will bring Joe's tone, as well as his individual contributions, to the
forefront of the field. I cannot imagine a better starting place for a student of
the subject.

(Glenn Shafer, Department of Accounting and Information Systems, Rutgers University
School of Business)

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)

Uncertainty is a central topic in many domains, such as economics, logic,
artificial intelligence, and statistics. It takes an omniscientist such as Joe
Halpern to treat this topic in full. His book is a rich source of unique insights,
offering unexpected connections between different fields.

(Peter P. Wakker, Department of Economics, University of Amsterdam)

Reiter's new book, Knowledge in Action, offers the
first systematic account of the logical approach to cognitive robotics, a field that
he and his colleagues have developed over the past decade. The unique feature of
this approach rests in its capacity to admit specifications in the form of
meaningful knowledge fragments, to piece those fragments together by logical and
probabilistic inferences, and to use those inferences to guide both manipulative and
perceptual actions by programmable agents. A must for anyone concerned with the
foundations of common sense knowledge or the design of autonomous dynamical

(Judea Pearl, Computer Science Department, University of California, Los

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, University of Konstanz)

Reasoning about Uncertainty is a very valuable
synthesis of the mathematics of uncertainty as it has developed in a number of
related fields -- probability, statistics, computer science, game theory, artificial
intelligence, and philosophy. Researchers in all of these fields will find this a
very useful book -- both for its elegant treatment of technical results and for its
illuminating conceptual discussions.

(Adam Brandenburger, J.P. Valles Professor of Business Economics and Strategy,
Stern School of Business, New York University)

About the Author

Joseph Y. Halpern is Professor of Computer Science at Cornell University.

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Product Details

  • Paperback: 497 pages
  • Publisher: The MIT Press; Revised edition (August 12, 2005)
  • Language: English
  • ISBN-10: 0262582597
  • ISBN-13: 978-0262582599
  • Product Dimensions: 8 x 1 x 9 inches
  • Shipping Weight: 1.7 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #438,697 in Books (See Top 100 in Books)

More About the Author

Joe Halpern was born in Israel, and emigrated to Canada at the age of four. He received a B.Sc. in mathematics from the University of Toronto in 1975 and a Ph.D. in mathematics from Harvard in 1981. In between, he spent two years as the head of the Mathematics Department at Bawku Secondary School, in Ghana.
After a year as a visiting scientist at MIT, he joined the IBM Almaden
Research Center in 1982. In 1996, he moved to Cornell University, where he is a professor in Computer Science and (as of July, 2010) the department chair.

He has received a number of awards: the ACM SIGART Autonomous Agents Research Award in 2011, the Dijkstra Prize (joint with Yoram Moses) in 2009, the
ACM/AAAI Newell Award in 2008, the Godel Prize (joint with Yoram Moses) in 1997, the Publishers' Prize for Best Paper at at the International Joint Conference on Artificial Intelligence in 1985 and in 1989, a best paper award at the Conference on Knowledge Representation and Reasoning in 2006 and 2012, and two IBM Outstanding Innovation Awards. He is a Fellow of AAAI (Association for the Advancement of Artificial Intelligence), AAAS (American Association for the Advancement of Science), and ACM (Association for Computing Machinery). He was editor-in-chief of Journal of the ACM, and has served as an editor for many other journals.

Besides all the academics, Halpern likes to write music, travel, read, and hang out with his kids. He lives in Ithaca, New York.

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Top Customer Reviews

Format: Paperback Verified Purchase
If you're completely at home with first-order logic and with probability, you're may be ready to extend some of those ideas. This book examines a range of topics that push logic and probability into wider, more interesting areas.

After a brief introduction, Halpern introduces upper and lower probabilities representing partial knowledge, and other measures representing belief, plausibility, possibility, and necessity. These are built up in a rigorous way, but with plenty of physical significance at each step - these aren't just axiomatic systems put together for their inherent elegance. The next few chapters build up a logical sequence of constructs around these measures, including independence, conditioning, and expectation. I expected to see confidence intervals generalized into these terms, but Halpern may have considered those to be exercises for the reader.

From these pieces, Halpern builds frameworks for real-world decision making. This includes the ability update knowledge (and ignorance) in the presence of new facts. It also includes modal logics, based on the variability of "truth" according to the time at which an assertion is made or the person by whom it it made, and "counterfactuals" that reason about events that could have occurred but didn't. And, whenever Halpern presents a new approach, he's also careful to point out where its weaknesses are.

This isn't for beginners, by any means. The successful reader is flexible about the axioms to use in an analytic system, and is able and willing to follow along with dense logical notation. One should not expect this to cover the whole world of soft logics - traditional fuzziness gets only brief mention, for example.
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Format: Paperback
This book guides you through formal systems useful for reasoning about uncertainty. If you've ever wondered about the rationale for probability theory or for ways to overcome its limitation, this is the book for you.

The author made an effort to make the book as self-contained as possible (a remarkable achievement given what it covers), so this book is very clear. The examples are short, but illuminating and motivating, so this book is interesting. The author always tries to justify why the axioms of a theory were chosen a certain way, so this book is insightful.

Even if you have just a passing interest in probability theory, I highly recommend this book. It will not only give you reasons for the definitions in probability theory, but also powerful alternative (and often complementary) ways of reasoning about uncertainty.
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Format: Paperback Verified Purchase
I was hoping for a more applied type of book and it is definitely not that. It has a lot of math theory (a little contrary to the Amazon info) and is definitely not for the math faint of heart. It implies that there isn't much math background required; but unless you have a strong background in the nomenclature and theory of sets then you'll be lost in the first few pages. I don't have a strong background in set theory so it has been very slow and a bit agonizing going. But, on the upside, it has given me a very wonderful and exciting bunch of insight into risk that I am glad I'm getting. It has been a fascinating read and adventure. I highly recommend it if you can handle the math.
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