Logic in Games

by van Benthem

ISBN: 9780262320306 | Copyright 2014

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This book draws on ideas from philosophical logic, computational logic, multi-agent systems, and game theory to offer a comprehensive account of logic and games viewed in two complementary ways. It examines the logic of games: the development of sophisticated modern dynamic logics that model information flow, communication, and interactive structures in games. It also examines logic as games: the idea that logical activities of reasoning and many related tasks can be viewed in the form of games. In doing so, the book takes up the "intelligent interaction" of agents engaging in competitive or cooperative activities and examines the patterns of strategic behavior that arise. It develops modern logical systems that can analyze information-driven changes in players' knowledge and beliefs, and introduces the "Theory of Play" that emerges from the combination of logic and game theory. This results in a new view of logic itself as an interactive rational activity based on reasoning, perception, and communication that has particular relevance for games. Logic in Games, based on a course taught by the author at Stanford University, the University of Amsterdam, and elsewhere, can be used in advanced seminars and as a resource for researchers.

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Contents (pg. v)
Preface (pg. xv)
Introduction: Exploring the Realm of Logic in Games (pg. 1)
I Game Logics and Process Structure (pg. 31)
Introduction to Part I (pg. 33)
1 Games as Processes: Definability and Invariance (pg. 35)
2 Preference, Game Solution, and Best Action (pg. 53)
3 Games with Imperfect Information (pg. 67)
4 Making Strategies Explicit (pg. 85)
5 Infinite Games and Temporal Evolution (pg. 103)
6 From Games to Models for Games (pg. 121)
Conclusion to Part I (pg. 145)
II Logical Dynamics and Theory of Play (pg. 147)
Introduction to Part II (pg. 149)
7 Logical Dynamics in a Nutshell (pg. 151)
8 Deliberation as Iterated Update (pg. 181)
9 Dynamic-Epistemic Mechanisms at Play (pg. 199)
10 Toward a Theory of Play (pg. 227)
Conclusion to Part II (pg. 249)
III Players' Powers and Strategic Games (pg. 251)
Introduction to Part III (pg. 253)
11 Forcing Powers (pg. 255)
12 Matrix Games and Their Logics (pg. 275)
13 Rational Dynamics for Strategic Games (pg. 299)
Conclusion to Part III (pg. 311)
IV Logic Games (pg. 313)
Introduction to Part IV (pg. 315)
14 Formula Evaluation (pg. 317)
15 Model Comparison (pg. 335)
16 Model Construction (pg. 351)
17 Argumentation and Dialogue (pg. 363)
18 General Lines through Logic Games (pg. 379)
Conclusion to Part IV (pg. 397)
V Operations on Games (pg. 399)
Introduction to Part V (pg. 401)
19 Dynamic Logic of Sequential Game Operations (pg. 403)
20 Linear Logic of Parallel Game Operations (pg. 427)
Conclusion to Part V (pg. 443)
VI Comparisons and Merges (pg. 445)
Introduction to Part VI (pg. 447)
21 Logic Games with Imperfect Information (pg. 449)
22 Knowledge Games (pg. 467)
23 Sabotage Games and Computation (pg. 477)
24 Logic Games Can Represent Game Logics (pg. 487)
25 Merging Logic Games with Game Logics (pg. 495)
Conclusion to Part VI (pg. 507)
VII Conclusion (pg. 509)
Conclusion (pg. 511)
Bibliography (pg. 515)
Index (pg. 543)
Contents (pg. v)
Preface (pg. xv)
Introduction: Exploring the Realm of Logic in Games (pg. 1)
I Game Logics and Process Structure (pg. 31)
Introduction to Part I (pg. 33)
1 Games as Processes: Definability and Invariance (pg. 35)
2 Preference, Game Solution, and Best Action (pg. 53)
3 Games with Imperfect Information (pg. 67)
4 Making Strategies Explicit (pg. 85)
5 Infinite Games and Temporal Evolution (pg. 103)
6 From Games to Models for Games (pg. 121)
Conclusion to Part I (pg. 145)
II Logical Dynamics and Theory of Play (pg. 147)
Introduction to Part II (pg. 149)
7 Logical Dynamics in a Nutshell (pg. 151)
8 Deliberation as Iterated Update (pg. 181)
9 Dynamic-Epistemic Mechanisms at Play (pg. 199)
10 Toward a Theory of Play (pg. 227)
Conclusion to Part II (pg. 249)
III Players' Powers and Strategic Games (pg. 251)
Introduction to Part III (pg. 253)
11 Forcing Powers (pg. 255)
12 Matrix Games and Their Logics (pg. 275)
13 Rational Dynamics for Strategic Games (pg. 299)
Conclusion to Part III (pg. 311)
IV Logic Games (pg. 313)
Introduction to Part IV (pg. 315)
14 Formula Evaluation (pg. 317)
15 Model Comparison (pg. 335)
16 Model Construction (pg. 351)
17 Argumentation and Dialogue (pg. 363)
18 General Lines through Logic Games (pg. 379)
Conclusion to Part IV (pg. 397)
V Operations on Games (pg. 399)
Introduction to Part V (pg. 401)
19 Dynamic Logic of Sequential Game Operations (pg. 403)
20 Linear Logic of Parallel Game Operations (pg. 427)
Conclusion to Part V (pg. 443)
VI Comparisons and Merges (pg. 445)
Introduction to Part VI (pg. 447)
21 Logic Games with Imperfect Information (pg. 449)
22 Knowledge Games (pg. 467)
23 Sabotage Games and Computation (pg. 477)
24 Logic Games Can Represent Game Logics (pg. 487)
25 Merging Logic Games with Game Logics (pg. 495)
Conclusion to Part VI (pg. 507)
VII Conclusion (pg. 509)
Conclusion (pg. 511)
Bibliography (pg. 515)
Index (pg. 543)
Contents (pg. v)
Preface (pg. xv)
Introduction: Exploring the Realm of Logic in Games (pg. 1)
I Game Logics and Process Structure (pg. 31)
Introduction to Part I (pg. 33)
1 Games as Processes: Definability and Invariance (pg. 35)
2 Preference, Game Solution, and Best Action (pg. 53)
3 Games with Imperfect Information (pg. 67)
4 Making Strategies Explicit (pg. 85)
5 Infinite Games and Temporal Evolution (pg. 103)
6 From Games to Models for Games (pg. 121)
Conclusion to Part I (pg. 145)
II Logical Dynamics and Theory of Play (pg. 147)
Introduction to Part II (pg. 149)
7 Logical Dynamics in a Nutshell (pg. 151)
8 Deliberation as Iterated Update (pg. 181)
9 Dynamic-Epistemic Mechanisms at Play (pg. 199)
10 Toward a Theory of Play (pg. 227)
Conclusion to Part II (pg. 249)
III Players' Powers and Strategic Games (pg. 251)
Introduction to Part III (pg. 253)
11 Forcing Powers (pg. 255)
12 Matrix Games and Their Logics (pg. 275)
13 Rational Dynamics for Strategic Games (pg. 299)
Conclusion to Part III (pg. 311)
IV Logic Games (pg. 313)
Introduction to Part IV (pg. 315)
14 Formula Evaluation (pg. 317)
15 Model Comparison (pg. 335)
16 Model Construction (pg. 351)
17 Argumentation and Dialogue (pg. 363)
18 General Lines through Logic Games (pg. 379)
Conclusion to Part IV (pg. 397)
V Operations on Games (pg. 399)
Introduction to Part V (pg. 401)
19 Dynamic Logic of Sequential Game Operations (pg. 403)
20 Linear Logic of Parallel Game Operations (pg. 427)
Conclusion to Part V (pg. 443)
VI Comparisons and Merges (pg. 445)
Introduction to Part VI (pg. 447)
21 Logic Games with Imperfect Information (pg. 449)
22 Knowledge Games (pg. 467)
23 Sabotage Games and Computation (pg. 477)
24 Logic Games Can Represent Game Logics (pg. 487)
25 Merging Logic Games with Game Logics (pg. 495)
Conclusion to Part VI (pg. 507)
VII Conclusion (pg. 509)
Conclusion (pg. 511)
Bibliography (pg. 515)
Index (pg. 543)
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