Logic and Information


Author: Keith Devlin
Publisher: Cambridge University Press
ISBN: 9780521499712
Category: Computers
Page: 307
View: 1817

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In this provocative and ground-breaking book, Keith Devlin argues that in order to obtain a deeper understanding of the nature of intelligence and knowledge acquisition, we must broaden our concept of logic. Classical logic, beginning with the work of Aristotle, has developed into a powerful and rigorous mathematical theory with many applications in mathematics and computer science, but it has proved woefully inadequate in the search for artificial intelligence. The new kind of logic, also mathematically based, outlined by Professor Devlin is the culmination of collaborative research among some of the world's leading logicians, philosophers, linguists, psychologists, and computer scientists. It introduces the concepts of infon, a quantum of information, and situations, a dynamical generalization of sets, and is capable of handlng the issues involved in human communication, thought, speech, and machine information processing.

Logic and Computation

Interactive Proof with Cambridge LCF
Author: Lawrence C. Paulson
Publisher: Cambridge University Press
ISBN: 9780521395601
Category: Computers
Page: 320
View: 1590

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Logic and Computation is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of statements in a programming language. This book consists of two parts. Part I outlines the mathematical preliminaries: elementary logic and domain theory. They are explained at an intuitive level, giving references to more advanced reading. Part II provides enough detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach.

Topology Via Logic


Author: Steven Vickers
Publisher: Cambridge University Press
ISBN: 9780521576512
Category: Computers
Page: 200
View: 3485

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This is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.

Information Flow

The Logic of Distributed Systems
Author: Jon Barwise,Jerry Seligman
Publisher: Cambridge University Press
ISBN: 9780521583862
Category: Computers
Page: 274
View: 9693

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Information is a central topic in computer science, cognitive science, and philosophy. In spite of its importance in the "information age," there is no consensus on what information is, what makes it possible, and what it means for one medium to carry information about another. Drawing on ideas from mathematics, computer science, and philosophy, this book addresses the definition and place of information in society. The authors, observing that information flow is possible only within a connected distribution system, provide a mathematically rigorous, philosophically sound foundation for a science of information. They illustrate their theory by applying it to a wide range of phenomena, from file transfer to DNA, from quantum mechanics to speech act theory.

Modal Logic


Author: Patrick Blackburn,Maarten de Rijke,Yde Venema
Publisher: Cambridge University Press
ISBN: 1316101959
Category: Computers
Page: N.A
View: 5181

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This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.

Basic Proof Theory


Author: A. S. Troelstra,H. Schwichtenberg
Publisher: Cambridge University Press
ISBN: 9780521779111
Category: Computers
Page: 417
View: 4865

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Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.

Basic Simple Type Theory


Author: J. Roger Hindley
Publisher: Cambridge University Press
ISBN: 9780521465182
Category: Computers
Page: 186
View: 1804

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Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. By concentrating on the principles that make the theory work in practice, the author covers all the key ideas without getting involved in the complications of more advanced systems. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm that lies at the heart of every such system. Also featured are two other interesting algorithms that until now have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making it the first book at this level that can be used as an introduction to type theory for computer scientists.

Design Theory and Computer Science


Author: Subrata Dasgupta
Publisher: Cambridge University Press
ISBN: 9780521118156
Category: Computers
Page: 452
View: 317

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The author examines logic and methodology of design from the perspective of computer science. Computers provide the context for this examination both by discussion of the design process for hardware and software systems and by consideration of the role of computers in design in general. The central question posed by the author is whether or not we can construct a theory of design.

Advanced Topics in Bisimulation and Coinduction


Author: Davide Sangiorgi,Jan Rutten
Publisher: Cambridge University Press
ISBN: 1139502905
Category: Computers
Page: N.A
View: 1242

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Coinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.

Extensions of First-Order Logic


Author: Maria Manzano
Publisher: Cambridge University Press
ISBN: 9780521354356
Category: Computers
Page: 388
View: 3794

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This book introduces some extensions of classical first-order logic and applies them to reasoning about computer programs. The extensions considered are: second-order logic, many-sorted logic, w-logic, modal logic type theory and dynamic logic. These have wide applications in various areas of computer science, philosophy, natural language processing and artificial intelligence. Researchers in these areas will find this book a useful introduction and comparative treatment.

Proofs and Types


Author: Jean-Yves Girard,Yves Lafont,Paul Taylor
Publisher: Cambridge University Press
ISBN: 9780521371810
Category: Computers
Page: 192
View: 9744

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This text is an outgrowth of notes prepared by J. Y. Girard for a course at the University of Paris VII. It deals with the mathematical background of the application to computer science of aspects of logic (namely the correspondence between proposition & types). Combined with the conceptual perspectives of Girard's ideas, this sheds light on both the traditional logic material & its prospective applications to computer science. The book covers a very active & exciting research area, & it will be essential reading for all those working in logic & computer science.

Mathematical Theory of Domains


Author: V. Stoltenberg-Hansen,I. Lindström,E. R. Griffor
Publisher: Cambridge University Press
ISBN: 9780521383448
Category: Computers
Page: 349
View: 3012

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Domain theory is an established part of theoretical computer science, used in giving semantics to programming languages and logics. In mathematics and logic it has also proved to be useful in the study of algorithms. This book is devoted to providing a unified and self-contained treatment of the subject. The theory is presented in a mathematically precise manner which nevertheless is accessible to mathematicians and computer scientists alike. The authors begin with the basic theory including domain equations, various domain representations and universal domains. They then proceed to more specialized topics such as effective and power domains, models of lambda-calculus and so on. In particular, the connections with ultrametric spaces and the Kleene–Kreisel continuous functionals are made precise. Consequently the text will be useful as an introductory textbook (earlier versions have been class-tested in Uppsala, Gothenburg, Passau, Munich and Swansea), or as a general reference for professionals in computer science and logic.

Temporal Logics in Computer Science


Author: Stéphane Demri,Valentin Goranko,Martin Lange
Publisher: Cambridge University Press
ISBN: 1107028361
Category: Computers
Page: 780
View: 2951

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A comprehensive, modern and technically precise exposition of the theory and main applications of temporal logics in computer science.

Nominal Sets

Names and Symmetry in Computer Science
Author: Andrew M. Pitts
Publisher: Cambridge University Press
ISBN: 1107244684
Category: Computers
Page: N.A
View: 607

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Nominal sets provide a promising new mathematical analysis of names in formal languages based upon symmetry, with many applications to the syntax and semantics of programming language constructs that involve binding, or localising names. Part I provides an introduction to the basic theory of nominal sets. In Part II, the author surveys some of the applications that have developed in programming language semantics (both operational and denotational), functional programming and logic programming. As the first book to give a detailed account of the theory of nominal sets, it will be welcomed by researchers and graduate students in theoretical computer science.

Deductive and Declarative Programming


Author: Peter Padawitz
Publisher: Cambridge University Press
ISBN: 9780521032513
Category: Computers
Page: 288
View: 8029

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The book can be used for graduate courses or as a reference for researchers in formal methods, theorem-proving and declarative languages.

Derivation and Computation

Taking the Curry-Howard Correspondence Seriously
Author: H. Simmons
Publisher: Cambridge University Press
ISBN: 9780521771733
Category: Computers
Page: 384
View: 3659

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Introduction to simple type theory; 200 exercises with complete solutions.

The Logic of Typed Feature Structures

With Applications to Unification Grammars, Logic Programs and Constraint Resolution
Author: Bob Carpenter
Publisher: Cambridge University Press
ISBN: 9780521022545
Category: Computers
Page: 280
View: 4486

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This book develops the theory of typed feature structures and provides a logical foundation for logic programming and constraint-based reasoning systems.

Formal Methods in Artificial Intelligence


Author: Allan Ramsay
Publisher: CUP Archive
ISBN: 9780521424219
Category: Computers
Page: 292
View: 9624

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This book covers the background of classical logic, including the major meta-theorems, and the state of the art in theorem proving.