A comprehensive examination of the interfaces of logic, computer science, and game theory, drawing on twenty years of research on logic and games.
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.
Johan van Benthem is University Professor of Pure and Applied Logic at the University of Amsterdam and Henry Waldgrave Stuart Professor of Philosophy at Stanford University. He is the author of Language in Action: Categories, Lambdas, and Dynamic Logic (MIT Press), Exploring Logical Dynamics, Logical Dynamics of Information and Interaction, and other books.
Logic in Games by Johan van Benthem deals with an important topic: the connections between logic and game theory. This is a major work by a leading international scholar addressing issues of great significance.
Robin Clark, Professor of Linguistics, University of Pennsylvania
Johan van Benthem's Logic in Games offers a comprehensive picture of the main concepts, techniques, and results obtained in the last two decades in game theory—of their philosophical motivation and their range of applications. Van Benthem's purpose is twofold: to use logical tools to understand central notions in game theory and to use this deeper understanding of games to recast our basic logical notions as games in order to uncover their underlying structure and understand logical reasoning in its strategic aspects. This is a very thought-provoking book, extremely rich in ideas, examples, conceptual and technical innovations.
Gabriel Sandu, Professor of Theoretical Philosophy, University of Helsinki
Unique in its style and approach, *Logic in Games* is a substantial contribution to mathematical logic and game theory and offers new ideas that will be inspiring for researchers from many fields. This book is extremely rich, exciting, and interesting.
Erich Grädel, Mathematical Foundations of Computer Science, Department of Mathematics, RWTH Aachen University