How much do you know ? How much do you know about what you know ? How much do you know about what someone else knows ? How much that someone else knows about what you know about what she knows, and how much do you know about that ?We started with a very simple question about knowledge, and almost immediately the chain of questions lead to complicated and hard to comprehend ones. Classic logic teaches us how one can reason about truth and falsehood of statements, but can it help us if we want to reason about our (or someone else's) knowledge ? And if the answer to the last question is "yes", then how can we achieve this goal ?These are just a few of the questions, that served as motivation for the book Reasoning About Knowledge. In the book authors discuss the extentions of classical logic that encapsulate the desired meaning of the statements such as "I know X ", "I know that Alice knows X " and "Everyone knows that I know X ".In the first chapters the book provides a number of motivating examples which lead the reader to an informal understanding of the authors' concept of knowledge. After that the notion of knowledge is being formalized by introduction of modal operators for knowledge, common knowledge and distributed knowledge into the classic Propositional logic. Kripke structures are introduced as models at the same time and the obtained modal logics are then studied closely with respect to their soundeness and completeness properties, as well as the complexity of decision procedures.Once the general background is layed out, authors start discussing a variety of applications of knowledge-based reasoning to other problems in such fields as AI and Communications. A number of chapters of the book are devoted to discussing multi-agent systems and their behavior. A concept of Common Knowledge and its relation to Agreement and Cooperation between agents is also discussed.The more detailed summary of the book is provided below.
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Review of Reasoning About Knowledge by Ronald Fagin, Joseph Halpern, Yoram Moses and Moshe Verdi
Dekhtyar, Alexander
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, Volume 28 (4)
Association for Computing Machinery – Dec 1, 1997
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