Exploring Logical Dynamics
Exploring Logical Dynamics

Author: Johan F. A. K. van Benthem

Publisher: Center for the Study of Language and Information Publications

Published: 1996-08-28

Total Pages: 341

ISBN-13: 9781575860589

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This book is an exploration of current trends in logical theories of information flow across various fields, such as belief revision in computer science or dynamic semantics in linguistics. It provides one mathematical perspective encompassing all of these. This framework generates a new agenda of questions concerning dynamic inference and dynamic operators. The result is a mathematical theory of process models, simulations between these, and modal languages over them, which is developed in quite some detail. New results include theorems on expressive completeness, representation of styles of inference, and new kinds of decidable remodeling for standard logics. This theory is also confronted with practice in computer science, linguistics and philosophy.

Logical Dynamics of Information and Interaction
Logical Dynamics of Information and Interaction

Author: Johan van Benthem

Publisher: Cambridge University Press

Published: 2011-09-29

Total Pages: 387

ISBN-13: 1139500465

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This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science.

Johan van Benthem on Logic and Information Dynamics
Johan van Benthem on Logic and Information Dynamics

Author: Alexandru Baltag

Publisher: Springer

Published: 2014-08-27

Total Pages: 1072

ISBN-13: 3319060252

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This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations.

Logical Dynamics of Information and Interaction
Logical Dynamics of Information and Interaction

Author: Johan van Benthem

Publisher:

Published: 2014-05-14

Total Pages: 386

ISBN-13: 9781139190343

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This book develops a new view of logic as a theory of information-driven agency and intelligent interaction between many agents with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the dynamic stance' for these areas, as well as cognitive science."

Language in Action
Language in Action

Author: Johan van Benthem

Publisher: MIT Press

Published: 1995

Total Pages: 390

ISBN-13: 9780262720243

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Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities.

Logic in Games
Logic in Games

Author: Johan Van Benthem

Publisher: MIT Press

Published: 2014-01-24

Total Pages: 567

ISBN-13: 0262320304

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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.

Logic and the Modalities in the Twentieth Century
Logic and the Modalities in the Twentieth Century

Author: Dov M. Gabbay

Publisher: Elsevier

Published: 2006-05-10

Total Pages: 733

ISBN-13: 0080463037

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Logic and the Modalities in the Twentieth Century is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and artificial intelligence, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas. This volume is number seven in the eleven volume Handbook of the History of Logic. It concentrates on the development of modal logic in the 20th century, one of the most important undertakings in logic’s long history. Written by the leading researchers and scholars in the field, the volume explores the logics of necessity and possibility, knowledge and belief, obligation and permission, time, tense and change, relevance, and more. Both this volume and the Handbook as a whole are definitive reference tools for students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, artificial intelligence, for whom the historical background of his or her work is a salient consideration. · Detailed and comprehensive chapters covering the entire range of modal logic. · Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic.

Handbook of Logic and Language
Handbook of Logic and Language

Author: Johan van Benthem

Publisher:

Published: 1997-01-23

Total Pages: 0

ISBN-13: 9780262525718

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The twenty chapters in this book show both sides of the interaction between logic and language: how logical systems are designed and modified in response to linguistic needs, and how mathematical theory arises out of this process and affects subsequent linguistic theory. The combined study of logic and language goes back at least as far as the Middle Ages. In the last twenty-five years it has gained momentum with the formulation of Montague semantics and Generative Syntax, and the subsequent diversification of research programs. The Handbook of Logic and Language is the first comprehensive survey of the field. The twenty chapters show both sides of the interaction between logic and language: how logical systems are designed and modified in response to linguistic needs, and how mathematical theory arises out of this process and affects subsequent linguistic theory. Contributors N. Asher, D. Beaver, W. Buszkowski, D. de Jongh, J. E. Fenstad, J. Groenendijk, H. Hendriks, J. Higginbotham, J. Hintikka, T. M. V. Janssen, H. Kamp, E. J. Keenan, J. T. Lønning, E. Martin, M. J. Moortgat, L. S. Moss, R. Muskens, D. Osherson, B. H. Partee, F. J. Pelletier, W. C. Rounds, G. Sandu, J. Seligman, M. Steedman, M. Stokhof, R. H. Thomason, R. Turner, J. van Benthem, J. van Eijck, A. Visser, D. Westerståhl

Logical Methods
Logical Methods

Author: Greg Restall

Publisher: MIT Press

Published: 2023-01-03

Total Pages: 285

ISBN-13: 0262372703

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An accessible introduction to philosophical logic, suitable for undergraduate courses and above. Rigorous yet accessible, Logical Methods introduces logical tools used in philosophy—including proofs, models, modal logics, meta-theory, two-dimensional logics, and quantification—for philosophy students at the undergraduate level and above. The approach developed by Greg Restall and Shawn Standefer is distinct from other texts because it presents proof construction on equal footing with model building and emphasizes connections to other areas of philosophy as the tools are developed. Throughout, the material draws on a broad range of examples to show readers how to develop and master tools of proofs and models for propositional, modal, and predicate logic; to construct and analyze arguments and to find their structure; to build counterexamples; to understand the broad sweep of formal logic’s development in the twentieth and twenty-first centuries; and to grasp key concepts used again and again in philosophy. This text is essential to philosophy curricula, regardless of specialization, and will also find wide use in mathematics and computer science programs. Features: An accessible introduction to proof theory for readers with no background in logic Covers proofs, models, modal logics, meta-theory, two-dimensional logics, quantification, and many other topics Provides tools and techniques of particular interest to philosophers and philosophical logicians Features short summaries of key concepts and skills at the end of each chapter Offers chapter-by-chapter exercises in two categories: basic, designed to reinforce important ideas; and challenge, designed to push students’ understanding and developing skills in new directions