Formal ways of representing uncertainty and various logics for reasoning about it; updated with new material on weighted probability measures, complexity-theoretic considerations, and other topics. In order to deal with uncertainty 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. Halpern surveys possible formal systems for representing uncertainty, including probability measures, possibility measures, and plausibility measures; considers the updating of beliefs based on changing information and the relation to Bayes' theorem; and discusses qualitative, quantitative, and plausibilistic Bayesian networks. This second edition has been updated to reflect Halpern's recent research. New material includes a consideration of weighted probability measures and how they can be used in decision making; analyses of the Doomsday argument and the Sleeping Beauty problem; modeling games with imperfect recall using the runs-and-systems approach; a discussion of complexity-theoretic considerations; the application of first-order conditional logic to security. Reasoning about Uncertainty is accessible and relevant to researchers and students in many fields, including computer science, artificial intelligence, economics (particularly game theory), mathematics, philosophy, and statistics.

The field of Artificial Intelligence has changed a great deal since the 80s, and arguably no one has played a larger role in that change than Judea Pearl. Judea Pearl's work made probability the prevailing language of modern AI and, perhaps more significantly, it placed the elaboration of crisp and meaningful models, and of effective computational mechanisms, at the center of AI research. This book is a collection of articles in honor of Judea Pearl, written by close colleagues and former students. Its three main parts, heuristics, probabilistic reasoning, and causality, correspond to the titles of the three ground-breaking books authored by Judea, and are followed by a section of short reminiscences. In this volume, leading authors look at the state of the art in the fields of heuristic, probabilistic, and causal reasoning, in light of Judea's seminal contributors. The authors list include Blai Bonet, Eric Hansen, Robert Holte, Jonathan Schaeffer, Ariel Felner, Richard Korf, Austin Parker, Dana Nau, V. S. Subrahmanian, Hector Geffner, Ira Pohl, Adnan Darwiche, Thomas Dean, Rina Dechter, Bozhena Bidyuk, Robert Matescu, Emma Rollon, Michael I. Jordan, Michael Kearns, Daphne Koller, Brian Milch, Stuart Russell, Azaria Paz, David Poole, Ingrid Zukerman, Carlos Brito, Philip Dawid, Felix Elwert, Christopher Winship, Michael Gelfond, Nelson Rushton, Moises Goldszmidt, Sander Greenland, Joseph Y. Halpern, Christopher Hitchcock, David Heckerman, Ross Shachter, Vladimir Lifschitz, Thomas Richardson, James Robins, Yoav Shoham, Peter Spirtes, Clark Glymour, Richard Scheines, Robert Tillman, Wolfgang Spohn, Jian Tian, Ilya Shpitser, Nils Nilsson, Edward T. Purcell, and David Spiegelhalter.

Reasoning about knowledge--particularly the knowledge of agents who reason about the world and each other's knowledge--was once the exclusive province of philosophers and puzzle solvers. More recently, this type of reasoning has been shown to play a key role in a surprising number of contexts, from understanding conversations to the analysis of distributed computer algorithms.Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed systems, artificial intelligence, and game theory. It brings eight years of work by the authors into a cohesive framework for understanding and analyzing reasoning about knowledge that is intuitive, mathematically well founded, useful in practice, and widely applicable. The book is almost completely self-contained and should be accessible to readers in a variety of disciplines, including computer science, artificial intelligence, linguistics, philosophy, cognitive science, and game theory. Each chapter includes exercises and bibliographic notes.

A new approach for defining causality and such related notions as degree of responsibility, degrees of blame, and causal explanation. Causality plays a central role in the way people structure the world; we constantly seek causal explanations for our observations. But what does it even mean that an event C "actually caused" event E? The problem of defining actual causation goes beyond mere philosophical speculation. For example, in many legal arguments, it is precisely what needs to be established in order to determine responsibility. The philosophy literature has been struggling with the problem of defining causality since Hume. In this book, Joseph Halpern explores actual causality, and such related notions as degree of responsibility, degree of blame, and causal explanation. The goal is to arrive at a definition of causality that matches our natural language usage and is helpful, for example, to a jury deciding a legal case, a programmer looking for the line of code that cause some software to fail, or an economist trying to determine whether austerity caused a subsequent depression. Halpern applies and expands an approach to causality that he and Judea Pearl developed, based on structural equations. He carefully formulates a definition of causality, and building on this, defines degree of responsibility, degree of blame, and causal explanation. He concludes by discussing how these ideas can be applied to such practical problems as accountability and program verification. Technical details are generally confined to the final section of each chapter and can be skipped by non-mathematical readers.