Exploring Logical Dynamics
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Author | : J. F. A. K. van Benthem |
Publisher | : Stanford Univ Center for the Study |
Total Pages | : 329 |
Release | : 1996-01-01 |
Genre | : Philosophy |
ISBN | : 9781575860596 |
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.
Author | : Johan van Benthem |
Publisher | : Cambridge University Press |
Total Pages | : 387 |
Release | : 2011-09-29 |
Genre | : Mathematics |
ISBN | : 1139500465 |
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.
Author | : Dov M. Gabbay |
Publisher | : Elsevier |
Total Pages | : 733 |
Release | : 2006-05-10 |
Genre | : Mathematics |
ISBN | : 0080463037 |
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.
Author | : Johan Van Benthem |
Publisher | : MIT Press |
Total Pages | : 567 |
Release | : 2014-01-24 |
Genre | : Computers |
ISBN | : 0262320304 |
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.
Author | : Greg Restall |
Publisher | : MIT Press |
Total Pages | : 285 |
Release | : 2023-01-03 |
Genre | : Philosophy |
ISBN | : 0262372703 |
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
Author | : Alexandru Baltag |
Publisher | : Springer |
Total Pages | : 1072 |
Release | : 2014-08-27 |
Genre | : Philosophy |
ISBN | : 3319060252 |
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.
Author | : Katalin Bimbo |
Publisher | : Springer |
Total Pages | : 469 |
Release | : 2016-04-02 |
Genre | : Philosophy |
ISBN | : 3319293001 |
This book celebrates and expands on J. Michael Dunn’s work on informational interpretations of logic. Dunn, in his Ph.D. thesis (1966), introduced a semantics for first-degree entailments utilizing the idea that a sentence can provide positive or negative information about a topic, possibly supplying both or neither. He later published a related interpretation of the logic R-mingle, which turned out to be one of the first relational semantics for a relevance logic. An incompatibility relation between information states lends itself to a definition of negation and it has figured into Dunn's comprehensive investigations into representations of various negations. The informational view of semantics is also a prominent theme in Dunn’s research on other logics, such as quantum logic and linear logic, and led to the encompassing theory of generalized Galois logics (or "gaggles"). Dunn’s latest work addresses informational interpretations of the ternary accessibility relation and the very nature of information. The book opens with Dunn’s autobiography, followed by a list of his publications. It then presents a series of papers written by respected logicians working on different aspects of information-based logics. The topics covered include the logic R-mingle, which was introduced by Dunn, and its applications in mathematical reasoning as well as its importance in obtaining results for other relevance logics. There are also interpretations of the accessibility relation in the semantics of relevance and other non-classical logics using different notions of information. It also presents a collection of papers that develop semantics for various logics, including certain modal and many-valued logics. The publication of this book is well timed, since we are living in an "information age.” Providing new technical findings, intellectual history and careful expositions of intriguing ideas, it appeals to a wide audience of scholars and researchers.
Author | : Johan F.A.K. van Benthem |
Publisher | : Elsevier |
Total Pages | : 1169 |
Release | : 2010-12-17 |
Genre | : Mathematics |
ISBN | : 0444537279 |
The logical study of language is becoming more interdisciplinary, playing a role in fields such as computer science, artificial intelligence, cognitive science and game theory. This new edition, written by the leading experts in the field, presents an overview of the latest developments at the interface of logic and linguistics as well as a historical perspective. It is divided into three parts covering Frameworks, General Topics and Descriptive Themes. - Completely revised and updated - includes over 25% new material - Discusses the interface between logic and language - Many of the authors are creators or active developers of the theories
Author | : Petr Sojka |
Publisher | : Springer |
Total Pages | : 469 |
Release | : 2003-07-31 |
Genre | : Computers |
ISBN | : 3540453237 |
The workshop series on Text, Speech and Dialogue originated in 1998 with the ?rst TSD1998 held in Brno, Czech Republic. This year’s TSD2000, already the third in the series, returns to Brno and to its organizers from the Faculty of Informatics at the Masaryk University. As shown by the ever growing interest in TSD series, this annual workshop developed into the prime meeting of speech and language researchers from both sides of the former Iron Curtain, which provides a unique opportunity to get acquainted with the current activities in all aspects of language communication and to witness the amazing vitality of researchers from the former East Block countries. Thanks need to be extended to all who continue to make the TSD workshop series such a success: ?rst, to the authors themselves, without whom TSD2000 would not exist; next, to all organizations that support TSD2000, among them the International Speech Communication Association, the Faculty of Informatics at the Masaryk University in Brno and the Faculty of Applied Sciences, West Bohemia University in Plzen; ? and last but not least,to the organizers and members of the Program Committee who spentmuch effort to make TSD2000 success and who reviewed 131 contributions submitted from all corners of the world and accepted 75 out of them for presentation at the workshop. This book is evidence of the success of all involved.
Author | : Michiel Hazewinkel |
Publisher | : Springer Science & Business Media |
Total Pages | : 564 |
Release | : 2007-11-23 |
Genre | : Mathematics |
ISBN | : 0306483734 |
This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.