Reasoning about Uncertainty

Reasoning about Uncertainty

By Joseph Y. Halpern





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.


Out of Print ISBN: 9780262083201 497 pp. | 7 in x 9 in 12 illus.


Out of Print ISBN: 9780262582599 497 pp. | 7 in x 9 in 12 illus.


  • 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