Preface

This is a highly biased view of uncertainty. I have focused on topics that I found interesting and with which I was familiar, with a particular emphasis on topics on which I have done some research. (This is meant to be a partial apology for the rather large number of references in the bibliography that list "Halpern" as a coauthor. It gives a rather unbalanced view of the influence I have had on the field!)

I hope the book will be read by researchers in a number of disciplines, including computer science, artificial intelligence, economics (particularly game theory), mathematics, philosophy, and statistics. With this goal in mind, I have tried to make the book accessible to readers with widely differing backgrounds. Logicians and philosophers may well be comfortable with all the logic and have trouble with probability and random variables. Statisticians and economists may have just the opposite problem. The book should contain enough detail to make it almost completely self-contained. However, there is no question that having some background in both propositional logic and probability would be helpful (although a few weeks of each in a discrete mathematics course ought to suffice); for Chapter 11, a basic understanding of limits is also necessary.

This book is mathematical, in the sense that ideas are formalized in terms of definitions and theorems. On the other hand, the emphasis on the book is not on proving theorems. Rather, I have tried to focus on a certain philosophy for representing and reasoning about uncertainty. (References to where proofs of theorems can be found are given in the notes to each chapter; in many cases, the proofs are discussed in the exercises, with hints.)

Now comes the paragraph in the book that was perhaps the most pleasurable to write: the acknowledgments. I'd particularly like to thank my collaborators over the years on topics related to reasoning about uncertainty, including Fahiem Bacchus, Francis Chu, Ron Fagin, Nir Friedman, Adam Grove, Peter Gr nwald, Daphne Koller, Yoram Moses, Riccardo Pucella, Mark Tuttle, and Moshe Vardi. There would have been no book to write if it hadn't been for the work we did together, and I wouldn't have been inspired to write the book if the work hadn't been so much fun. Thanks to many students and colleagues who gave me comments and found typos, including Fokko von de Bult, Willem Conradie, Francis Chu, Christine Chung, Dieter Denneberg, Pablo Fierens, Li Li, Lori Lorigo, Fabrice Nauze, Sabina Petride, Riccardo Pucella, Joshua Sack, Richard Shore, Sebastian Silgardo, Jan de Vos, Peter Wakker, and Eduardo Zambrano. Riccardo, in particular, gave detailed comments and went out of his way to make suggestions that greatly improved the presentation. Of course, the responsibility for all remaining bugs are mine. (I don't know of any as I write this, but I am quite sure there are still some there.) Thanks to those who funded much of the research reported here: Abe Waksman at AFOSR, Ralph Wachter at ONR, and Larry Reeker and Ephraim Glinert at NSF. I would also like to acknowledge a Fulbright Fellowship and a Guggenheim Fellowship, which provided me with partial support during a sabbatical in 2001–2002, when I put the finishing touches to the book. And last but far from least, thanks to my family, who have put up with me coming home late for so many years. I'll try to be better.