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Reasoning about Uncertainty (MIT Press) Paperback – August 12, 2005
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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 systems.(Judea Pearl, Computer Science Department, University of California, Los Angeles)
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)
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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.Read more ›
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.