Reasoning about Uncertainty [Hardcover]

Joseph Y. Halpern (Author)

Book Description

Publication Date: September 12, 2003

Uncertainty is a fundamental and unavoidable feature of daily life; in order to deal with uncertaintly 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; the material is accessible and relevant to researchers and students in many fields, including computer science, artificial intelligence, economics (particularly game theory), mathematics, philosophy, and statistics.Halpern begins by surveying possible formal systems for representing uncertainty, including probability measures, possibility measures, and plausibility measures. He considers the updating of beliefs based on changing information and the relation to Bayes' theorem; this leads to a discussion of qualitative, quantitative, and plausibilistic Bayesian networks. He considers not only the uncertainty of a single agent but also uncertainty in a multi-agent framework. Halpern then considers the formal logical systems for reasoning about uncertainty. He discusses knowledge and belief; default reasoning and the semantics of default; reasoning about counterfactuals, and combining probability and counterfactuals; belief revision; first-order modal logic; and statistics and beliefs. He includes a series of exercises at the end of each chapter.

Editorial Reviews

Review

"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

"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 commonsense knowledge or the design of autonomous dynamical systems."--Judea Pearl, Computer Science Department, University of California, Los Angeles

" 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

"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* 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.

Product Details

• Hardcover: 497 pages
• Publisher: The MIT Press (September 12, 2003)
• Language: English
• ISBN-10: 0262083205
• ISBN-13: 978-0262083201
• Product Dimensions: 9.4 x 7 x 1.2 inches
• Shipping Weight: 2.1 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: #1,578,424 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 (joint with Ronald Fagin) and in 1989, a best paper award at the Conference on Knowledge Representation and Reasoning in 2006, 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.

Customer Reviews

Most Helpful Customer Reviews

24 of 27 people found the following review helpful:

4.0 out of 5 stars Deep look at the logic of uncertainty, March 27, 2006

By 

wiredweird "wiredweird" (Earth, or somewhere nearby) - See all my reviews
(HALL OF FAME REVIEWER)    (TOP 500 REVIEWER)   

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This review is from: Reasoning about Uncertainty (Paperback)

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. The best parts of this presentation extend familiar probabilistic terms (such as expectation) well beyond their original frameworks, creating a more unified view of various belief measures than I've seen elsewhere. If you have a serious interest in soft logic, formal reasoning, and mathematical tools for AI, I recommend this book very highly.

-- wiredweird

8 of 9 people found the following review helpful:

5.0 out of 5 stars clear, interesting, insightful, May 19, 2008

By 

Nada Amin (Cambridge, MA, USA) - See all my reviews
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This review is from: Reasoning about Uncertainty (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.

1 of 1 people found the following review helpful:

5.0 out of 5 stars Not what I had expected; but fascinating, July 26, 2010

By 

A. KEITH "space man" (Albuquerque, NM) - See all my reviews
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Amazon Verified Purchase

This review is from: Reasoning about Uncertainty (Paperback)

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.