Kooi Dynamic Epistemic Logic

1. Auflage 2007
ISBN: 978-1-4020-5839-4
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 296 Seiten

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.

Autoren/Hrsg.

Kooi, Barteld

Inhaltsverzeichnis

1;Contents;6
2;Preface;9
2.1;Acknowledgements;10
3;1 Introduction;12
3.1;1.1 Epistemic and Doxastic Logic;13
3.2;1.2 Dynamic Epistemic Logic;14
3.3;1.3 Information, Belief, and Knowledge;16
4;2 Epistemic Logic;22
4.1;2.1 Introduction;22
4.2;2.2 Basic System: S5;22
4.3;2.3 Group Notions of Knowledge;41
4.4;2.4 Logics for Belief;49
4.5;2.5 Notes;51
5;3 Belief Revision;54
5.1;3.1 Introduction;54
5.2;3.2 The AGM-approach;55
5.3;3.3 Possible Worlds Semantics for Information Change;66
5.4;3.4 Paradoxes of Introspective Belief Change;69
5.5;3.5 Dynamic Doxastic Logic;74
5.6;3.6 Notes;76
6;4 Public Announcements;78
6.1;4.1 Introduction;78
6.2;4.2 Examples;79
6.3;4.3 Syntax;83
6.4;4.4 Semantics;85
6.5;4.5 Principles of Public Announcement Logic;88
6.6;4.6 Announcement and Common Knowledge;92
6.7;4.7 Unsuccessful Updates;95
6.8;4.8 Axiomatisation;99
6.9;4.9 Knowledge and Belief;102
6.10;4.10 Muddy Children;104
6.11;4.11 Sum and Product;107
6.12;4.12 Russian Cards;108
6.13;4.13 Notes;115
7;5 Epistemic Actions;120
7.1;5.1 Introduction;120
7.2;5.2 Syntax;123
7.3;5.3 Semantics;126
7.4;5.4 Card Game Actions;137
7.5;5.5 Spreading Gossip;145
7.6;5.6 Notes;148
8;6 Action Models;151
8.1;6.1 Introduction;151
8.2;6.2 Action Models;159
8.3;6.3 Syntax of Action Model Logic;159
8.4;6.4 Semantics of Action Model Logic;161
8.5;6.5 Bisimilarity and Action Emulation;167
8.6;6.6 Validities and Axiomatisation;172
8.7;6.7 Epistemic Model Checking;176
8.8;6.8 Relational Actions and Action Models;180
8.9;6.9 Private Announcements;183
8.10;6.10 Notes;184
9;7 Completeness;187
9.1;7.1 Introduction;187
9.2;7.2 S5: The Basic Case;188
9.3;7.3 S5C: Dealing with Non-compactness;192
9.4;7.4 PA: Completeness by Translation;196
9.5;7.5 PAC: Induction on Complexity;199
9.6;7.6 AM: Translating Action Models;204
9.7;7.7 AMC: Generalising the Proof for PAC;206
9.8;7.8 Relativised Common Knowledge;211
9.9;7.9 Notes;218
10;8 Expressivity;220
10.1;8.1 Introduction;220
10.2;8.2 Basic Concepts;221
10.3;8.3 Bisimulation;224
10.4;8.4 Games;229
10.5;8.5 S5;233
10.6;8.6 S5C;236
10.7;8.7 PA;239
10.8;8.8 PAC;240
10.9;8.9 Non-deterministic Choice;244
10.10;8.10 AM;246
10.11;8.11 Relativised Common Knowledge;246
10.12;8.12 Notes;250
11;A Selected Answers to Exercises;252
11.1;Answers to Exercises from Chapter 2;252
11.2;Answers to Exercises from Chapter 3;255
11.3;Answers to Exercises from Chapter 4;258
11.4;Answers to Exercises from Chapter 5;263
11.5;Answers to Exercises from Chapter 6;266
11.6;Answers to Exercises from Chapter 7;268
11.7;Answers to Exercises from Chapter 8;271
12;References;273
13;Index;284