Dynamic Epistemic Logic (eBook)

Hans Van Ditmarsch, Wiebe Van Der Hoek, Barteld Kooi (Autoren)

eBook Download: PDF

2007 | 2008
XI, 296 Seiten
Springer Netherland (Verlag)
978-1-4020-5839-4 (ISBN)

Infos

Dynamic Epistemic Logic is the logic of knowledge change. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also offers exercises with answers. It is suitable for graduate courses in logic. Many examples, exercises, and thorough completeness proofs and expressivity results are included. A companion web page offers slides for lecturers and exams for further practice.

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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.

Inhalt

Contents 6
Preface 9
Acknowledgements 10
1 Introduction 12
1.1 Epistemic and Doxastic Logic 13
1.2 Dynamic Epistemic Logic 14
1.3 Information, Belief, and Knowledge 16
2 Epistemic Logic 22
2.1 Introduction 22
2.2 Basic System: S5 22
2.3 Group Notions of Knowledge 41
2.4 Logics for Belief 49
2.5 Notes 51
3 Belief Revision 54
3.1 Introduction 54
3.2 The AGM-approach 55
3.3 Possible Worlds Semantics for Information Change 66
3.4 Paradoxes of Introspective Belief Change 69
3.5 Dynamic Doxastic Logic 74
3.6 Notes 76
4 Public Announcements 78
4.1 Introduction 78
4.2 Examples 79
4.3 Syntax 83
4.4 Semantics 85
4.5 Principles of Public Announcement Logic 88
4.6 Announcement and Common Knowledge 92
4.7 Unsuccessful Updates 95
4.8 Axiomatisation 99
4.9 Knowledge and Belief 102
4.10 Muddy Children 104
4.11 Sum and Product 107
4.12 Russian Cards 108
4.13 Notes 115
5 Epistemic Actions 120
5.1 Introduction 120
5.2 Syntax 123
5.3 Semantics 126
5.4 Card Game Actions 137
5.5 Spreading Gossip 145
5.6 Notes 148
6 Action Models 151
6.1 Introduction 151
6.2 Action Models 159
6.3 Syntax of Action Model Logic 159
6.4 Semantics of Action Model Logic 161
6.5 Bisimilarity and Action Emulation 167
6.6 Validities and Axiomatisation 172
6.7 Epistemic Model Checking 176
6.8 Relational Actions and Action Models 180
6.9 Private Announcements 183
6.10 Notes 184
7 Completeness 187
7.1 Introduction 187
7.2 S5: The Basic Case 188
7.3 S5C: Dealing with Non-compactness 192
7.4 PA: Completeness by Translation 196
7.5 PAC: Induction on Complexity 199
7.6 AM: Translating Action Models 204
7.7 AMC: Generalising the Proof for PAC 206
7.8 Relativised Common Knowledge 211
7.9 Notes 218
8 Expressivity 220
8.1 Introduction 220
8.2 Basic Concepts 221
8.3 Bisimulation 224
8.4 Games 229
8.5 S5 233
8.6 S5C 236
8.7 PA 239
8.8 PAC 240
8.9 Non-deterministic Choice 244
8.10 AM 246
8.11 Relativised Common Knowledge 246
8.12 Notes 250
A Selected Answers to Exercises 252
Answers to Exercises from Chapter 2 252
Answers to Exercises from Chapter 3 255
Answers to Exercises from Chapter 4 258
Answers to Exercises from Chapter 5 263
Answers to Exercises from Chapter 6 266
Answers to Exercises from Chapter 7 268
Answers to Exercises from Chapter 8 271
References 273
Index 284

Produkt-Details

• Erscheint lt. Verlag: 6.5.2007
• Reihe/Serie: Synthese Library
• Reihe/Serie: Synthese Library
• Zusatzinfo: XI, 296 p.
• Verlagsort: Dordrecht
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
• Themenwelt: Geisteswissenschaften ► Philosophie ► Erkenntnistheorie / Wissenschaftstheorie
• Themenwelt: Geisteswissenschaften ► Philosophie ► Logik
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Informatik ► Web / Internet
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Schlagworte: Belief Revision • Common Knowledge • dynamic epistemic logic • epistemic actions • formal specification • Idea • Knowledge • Logic • multi-agent system • Multi-agent Systems • Subject
• ISBN-10: 1-4020-5839-X / 140205839X
• ISBN-13: 978-1-4020-5839-4 / 9781402058394