Reasoning about Uncertainty | 
| Author: Joseph Y. Halpern
Publisher: The MIT Press
Category: Book
List Price: $30.00
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Avg. Customer Rating:  2 reviews
Sales Rank: 96387
Media: Paperback
Number Of Items: 1
Pages: 497
Shipping Weight (lbs): 1.7
Dimensions (in): 8.9 x 7 x 1
ISBN: 0262582597
Dewey Decimal Number: 003.54
EAN: 9780262582599
ASIN: 0262582597
Publication Date: September 1, 2005
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Product Description
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.
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| Customer Reviews:
 clear, interesting, insightful May 19, 2008
1 out of 1 found this review helpful
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.
 Deep look at the logic of uncertainty March 28, 2006
20 out of 22 found this review helpful
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
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