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Reviewer: Julia E. Hodges

The main topic of this book is reasoning among a group of agents, as opposed to the reasoning that is done by a single agent in isolation. The book begins with an excellent discussion of the semantics of possible worlds, including realistic examples that serve their purpose well. Next, the authors provide formal proofs and algorithms regarding the properties of knowledge in possible worlds. They then extend their discussion to multi-agent systems and to the inclusion of actions and protocols. The authors illustrate that, in a multi-agent environment, one needs “common knowledge.” That is, to reason effectively, I need to know what I know, I need to know what the other agents know, I need to know that the other agents know that I know what they know, and so on. Common knowledge also includes agreements that agents may reach about disagreeing. The discussion of the different facets of common knowledge is augmented by both simple puzzles (such as a group of generals planning a battle, where some of the generals are loyal and some are traitors) and formal theorem proofs. In addition to common knowledge, the authors discuss distributed knowledge. Following their discussion of common knowledge, the authors devote a chapter to knowledge-based programming, including a formal comparison between standard programs and knowledge-based programs. They extend their definition of knowledge to include how knowledge evolves over time. They illustrate how one may construct abstract models for agents that do not necessarily know all of the logical consequences of their own knowledge. Finally, they revisit the concept of common knowledge, introducing the consideration of simultaneous events and how this can affect common knowledge. Exercises are provided at the end of each chapter. In addition, notes on the references that were used and additional references that are available are included with each chapter. The chapters are organized in a way that makes it easy for an instructor who uses this book as a textbook to exclude certain sections without confusing the students. Not only does this book make an excellent reference book for anyone interested in reasoning about knowledge, it should be appropriate as a textbook for a graduate-level course on this subject.