Barteld Kooi – författare
Dynamic Epistemic Logic
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Dynamic Epistemic Logic is the logic of knowledge change. This is not about one logical system, but about a whole family of logics that allows us to specify static and dynamic aspects of multi-agent systems. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also contains exercises including answers and is eminently suitable for graduate courses in logic.
A sweeping chapter-wise outline of the content of this book is the following. The chapter ''Introduction'' informs the reader about the history of the subject, and its relation to other disciplines. ''Epistemic Logic'' is an overview of multi-agent epistemic logic - the logic of knowledge - including modal operators for groups, such as general and common knowledge. ''Belief Revision'' is an overview on how to model belief revision, both in the ''traditional'' way and in a dynamic epistemic setting. ''Public Announcements'' is a detailed and comprehensive introduction to the logic of knowledge to which dynamic operators for truthful public announcement are added. Many interesting applications are also presented in this chapter: a form of cryptography for ideal agents also known as ''the Russian cards problem'', the sum-and-product riddle, etc. ''Epistemic Actions'' introduces a generalization of public announcement logic to more complex epistemic actions. A different perspective on that matter is independently presented in ''Action Models''. ''Completeness'' gives details on the completeness proof for the logics introduced in ''Epistemic Logic'', ''Public Announcements'', and ''Action Models''. ''Expressivity'' discusses various results on the expressive power of the logics presented.
Dynamic Epistemic Logic
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A group of 100 prisoners, all together in the prison dining area, are told that they will be all put in isolation cells and then will be interrogated one by one in a room containing a light with an on/off switch. The prisoners may communicate with one another by toggling the light switch (and that is the only way in which they can communicate). The light is initially switched off. There is no fixed order of interrogation, or interval between interrogations, and the same prisoner may be interrogated again at any stage. When interrogated, a prisoner can either do nothing, or toggle the light switch, or announce that all prisoners have been interrogated. If that announcement is true, the prisoners will (all) be set free, but if it is false, they will all be executed. While still in the dining room, and before the prisoners go to their isolation cells (forever), can the prisoners agree on a protocol that will set them free?
At first glance, this riddle may seem impossible to solve: how can all of the necessary information be transmitted by the prisoners using only a single light bulb? There is indeed a solution, however, and it can be found by reasoning about knowledge.
This book provides a guided tour through eleven classic logic puzzles that are engaging and challenging and often surprising in their solutions. These riddles revolve around the characters’ declarations of knowledge, ignorance, and the appearance that they are contradicting themselves in some way. Each chapter focuses on one puzzle, which the authors break down in order to guide the reader toward the solution.
For general readers and students with little technical knowledge of mathematics, One Hundred Prisoners and a Light Bulb will be an accessible and fun introduction to epistemic logic. Additionally, more advanced students and their teachers will find it to be a valuable reference text for introductory course work and further study.