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Dynamic epistemic logic. (English) Zbl 1156.03015

Synthese Library 337. Dordrecht: Springer (ISBN 978-1-4020-6908-6/pbk; 978-1-4020-5838-7/hbk). xi, 282 p. (2008).
This is an excellent and much needed introduction to recent advances in the logic of knowledge change. The book consists of 8 chapters, the first of which gives a brief introduction. Chapter 2 introduces epistemic logic both semantically (by means of Kripke structures) and syntactically (by means of modal logic). Group notions of knowledge, in particular common knowledge, are also discussed. Chapter 3 deals with the AGM approach to belief revision. Chapter 4 gives a comprehensive account of a logic of knowledge with dynamic operators for truthful public announcements. Chapter 5 proceeds to a generalization of public announcement logic to more complex epistemic actions, while Chapter 6 is devoted to the action model approach to describing epistemic actions. Chapter 7 contains the proofs of completeness for the logics introduced in Chapters 2, 4 and 6. Chapter 8 discusses various results on the expressive power of the logics presented in the previous chapters. An attractive feature of this book is the multitude of illustrative examples.

MSC:

03B42 Logics of knowledge and belief (including belief change)
03B45 Modal logic (including the logic of norms)
68T27 Logic in artificial intelligence
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
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