Logic, Convention, and Common Knowledge


Book Description

One of the fundamental theses of this book is that logical consequence and logical truth are not simply given, but arise as conventions among the users of logic. Thus Syverson explains convention within a game-theoretic framework, as a kind of equilibrium between the strategies of players in a game where they share common knowledge of events—a revisiting of Lewis's Convention that argues that convention can be reasonably treated as coordination equilibria. Most strikingly, a realistic solution is provided for Gray's classic coordination problem, wherein two generals can only communicate with each other through unreliable means.




Logic, Convention, and Common Knowledge


Book Description

One of the fundamental theses of this book is that logical consequence and logical truth are not simply given, but arise as conventions among the users of logic. Thus Syverson explains convention within a game-theoretic framework, as a kind of equilibrium between the strategies of players in a game where they share common knowledge of events—a revisiting of Lewis's Convention that argues that convention can be reasonably treated as coordination equilibria. Most strikingly, a realistic solution is provided for Gray's classic coordination problem, wherein two generals can only communicate with each other through unreliable means.




Reasoning About Knowledge


Book Description

Reasoning about knowledge—particularly the knowledge of agents who reason about the world and each other's knowledge—was once the exclusive province of philosophers and puzzle solvers. More recently, this type of reasoning has been shown to play a key role in a surprising number of contexts, from understanding conversations to the analysis of distributed computer algorithms. Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed systems, artificial intelligence, and game theory. It brings eight years of work by the authors into a cohesive framework for understanding and analyzing reasoning about knowledge that is intuitive, mathematically well founded, useful in practice, and widely applicable. The book is almost completely self-contained and should be accessible to readers in a variety of disciplines, including computer science, artificial intelligence, linguistics, philosophy, cognitive science, and game theory. Each chapter includes exercises and bibliographic notes.




Common Knowledge


Book Description

Photo opportunities, ten-second sound bites, talking heads and celebrity anchors: so the world is explained daily to millions of Americans. The result, according to the experts, is an ignorant public, helpless targets of a one-way flow of carefully filtered and orchestrated communication. Common Knowledge shatters this pervasive myth. Reporting on a ground-breaking study, the authors reveal that our shared knowledge and evolving political beliefs are determined largely by how we actively reinterpret the images, fragments, and signals we find in the mass media. For their study, the authors analyzed coverage of 150 television and newspaper stories on five prominent issues—drugs, AIDS, South African apartheid, the Strategic Defense Initiative, and the stock market crash of October 1987. They tested audience responses of more than 1,600 people, and conducted in-depth interviews with a select sample. What emerges is a surprisingly complex picture of people actively and critically interpreting the news, making sense of even the most abstract issues in terms of their own lives, and finding political meaning in a sophisticated interplay of message, medium, and firsthand experience. At every turn, Common Knowledge refutes conventional wisdom. It shows that television is far more effective at raising the saliency of issues and promoting learning than is generally assumed; it also undermines the assumed causal connection between newspaper reading and higher levels of political knowledge. Finally, this book gives a deeply responsible and thoroughly fascinating account of how the news is conveyed to us, and how we in turn convey it to others, making meaning of at once so much and so little. For anyone who makes the news—or tries to make anything of it—Common Knowledge promises uncommon wisdom.




Theoretical Aspects of Reasoning About Knowledge


Book Description

Theoretical Aspects of Reasoning About Knowledge contains the proceedings of the Fifth Conference on Theoretical Aspects of Reasoning About Knowledge (TARK 1994) held in Pacific Grove, California, on March 13-16, 1994. The conference provided a forum for discussing the theoretical aspects of reasoning about knowledge and tackled topics ranging from the logic of iterated belief revision and backwards forward induction to information acquisition from multi-agent resources, infinitely epistemic logic, and coherent belief revision in games. Comprised of 23 chapters, this book begins with a review of situation calculus and a solution to the frame problem, along with the use of a regression method for reasoning about the effect of actions. A novel programming language for high-level robotic control is described, along with a knowledge-based framework for belief change. Subsequent chapters deal with consistent belief reasoning in the presence of inconsistency; an epistemic logic of situations; an axiomatic approach to the logical omniscience problem; and an epistemic proof system for parallel processes. Inductive learning, knowledge asymmetries, and convention are also examined. This monograph will be of interest to both students and practitioners in the fields of artificial intelligence and computer science.




Language in Action


Book Description

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.




Epistemic Logic and the Theory of Games and Decisions


Book Description

The convergence of game theory and epistemic logic has been in progress for two decades and this book explores this further by gathering specialists from different professional communities, i.e., economics, mathematics, philosophy, and computer science. This volume considers the issues of knowledge, belief and strategic interaction, with each contribution evaluating the foundational issues. In particular, emphasis is placed on epistemic logic and the representative topics of backward induction arguments and syntax/semantics and the logical omniscience problem. Part I of this collection deals with iterated knowledge in the multi-agent context, and more particularly with common knowledge. The first two papers in Part II of the collection address the so-called logical omniscience problem, a problem which has attracted much attention in the recent epistemic logic literature, and is pertinent to some of the issues discussed by decision theorists under the heading 'bounded rationality'. The remaining two chapters of section II provide two quite different angles on the strength of S5 (or the partitional model of information)- and so two different reasons for eschewing the strong form of logical omniscience implicit in S5. Part III gives attention to application to game theory and decision theory.




Impossible?


Book Description

In Nonplussed!, popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable—and all of it mathematically irrefutable. Whenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly—why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion—how is this possible? What does the game show Let's Make A Deal reveal about the unexpected hazards of decision-making? What can the game of cricket teach us about the surprising behavior of the law of averages? These are some of the counterintuitive mathematical occurrences that readers encounter in Impossible? Havil ventures further than ever into territory where intuition can lead one astray. He gathers entertaining problems from probability and statistics along with an eclectic variety of conundrums and puzzlers from other areas of mathematics, including classics of abstract math like the Banach-Tarski paradox. These problems range in difficulty from easy to highly challenging, yet they can be tackled by anyone with a background in calculus. And the fascinating history and personalities associated with many of the problems are included with their mathematical proofs. Impossible? will delight anyone who wants to have their reason thoroughly confounded in the most astonishing and unpredictable ways.




Designing Asynchronous Circuits Using NULL Convention Logic (NCL)


Book Description

Designing Asynchronous Circuits using NULL Convention Logic (NCL) begins with an introduction to asynchronous (clockless) logic in general, and then focuses on delay-insensitive asynchronous logic design using the NCL paradigm. The book details design of input-complete and observable dual-rail and quad-rail combinational circuits, and then discusses implementation of sequential circuits, which require datapath feedback. Next, throughput optimization techniques are presented, including pipelining, embedding registration, early completion, and NULL cycle reduction. Subsequently, low-power design techniques, such as wavefront steering and Multi-Threshold CMOS (MTCMOS) for NCL, are discussed. The book culminates with a comprehensive design example of an optimized Greatest Common Divisor circuit. Readers should have prior knowledge of basic logic design concepts, such as Boolean algebra and Karnaugh maps. After studying this book, readers should have a good understanding of the differences between asynchronous and synchronous circuits, and should be able to design arbitrary NCL circuits, optimized for area, throughput, and power. Table of Contents: Introduction to Asynchronous Logic / Overview of NULL Convention Logic (NCL) / Combinational NCL Circuit Design / Sequential NCL Circuit Design / NCL Throughput Optimization / Low-Power NCL Design / Comprehensive NCL Design Example