Computability and Logic

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Author: George S. Boolos,John P. Burgess,Richard C. Jeffrey

Publisher: Cambridge University Press

ISBN: 9780521007580

Category: Philosophy

Page: 356

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This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book has become a classic because of its accessibility to students without a mathematical background, and because it covers not simply the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem. John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer.

Computability and Logic

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Author: George Boolos,Richard C. Jeffrey

Publisher: CUP Archive

ISBN: 9780521204026

Category: Computable functions

Page: 262

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Berechenbarkeit, Komplexität, Logik

Eine Einführung in Algorithmen, Sprachen und Kalküle unter besonderer Berücksichtigung ihrer Komplexität

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Author: Egon Börger

Publisher: Springer-Verlag

ISBN: 3322877779

Category: Computers

Page: 470

View: 4835

Computability, Complexity, Logic

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Author: E. Börger

Publisher: Elsevier

ISBN: 9780080887043

Category: Mathematics

Page: 591

View: 6982

The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems. The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory. It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions.

Combinatorics, Computability and Logic

Proceedings of the Third International Conference on Combinatorics, Computability and Logic, (DMTCS’01)

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Author: C.S. Calude,M.J. Dinneen,S. Sburlan

Publisher: Springer Science & Business Media

ISBN: 1447107179

Category: Mathematics

Page: 251

View: 6834

This volume contains the papers presented at the Third Discrete Mathematics and Theoretical Computer Science Conference (DMTCS1), which was held at 'Ovidius'University Constantza, Romania in July 2001. The conference was open to all areas of discrete mathematics and theoretical computer science, and the papers contained within this volume cover topics such as: abstract data types and specifications; algorithms and data structures; automata and formal languages; computability, complexity and constructive mathematics; discrete mathematics, combinatorial computing and category theory; logic, nonmonotonic logic and hybrid systems; molecular computing.

Models and Computability

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Author: S. Barry Cooper,John K. Truss

Publisher: Cambridge University Press

ISBN: 9780521635509

Category: Mathematics

Page: 419

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Second of two volumes providing a comprehensive guide to the current state of mathematical logic.

Berechenbarkeit

Rekursive und Programmierbare Funktionen

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Author: Walter Felscher

Publisher: Springer-Verlag

ISBN: 3642780199

Category: Computers

Page: 478

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Dieses Lehrbuch behandelt verständlich, umfassend und modern die Theorie der Berechenbarkeit, ein klassisches Gebiet der Mathematischen Logik, das als Grundlagengebiet auch für die Informatik von höchster Bedeutung ist. Lebendig und didaktisch klar wird das Studium der berechenbaren Funktionen auf dem Programmbegriff aufgebaut. Dabei sind die Induktion als Beweisprinzip und die Rekursion als Konstruktionsprinzip die beiden grundlegenden Werkzeuge für den Umgang mit Zahlen und Funktionen. Obwohl über eine gewisse Vertrautheit mit der mathematischen Argumentationsweise hinaus keine inhaltlichen Kenntnisse aus der Mathematik oder der Informatik vorausgesetzt werden, findet auch der Kenner eine durch viele neuartige Details angereicherte und an neuesten Ergebnissen orientierte Darstellung.

Logic

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Author: Paul Tomassi

Publisher: Routledge

ISBN: 1134705913

Category: Philosophy

Page: 432

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Bringing elementary logic out of the academic darkness into the light of day, Paul Tomassi makes logic fully accessible for anyone attempting to come to grips with the complexities of this challenging subject. Including student-friendly exercises, illustrations, summaries and a glossary of terms, Logic introduces and explains: * The Theory of Validity * The Language of Propositional Logic * Proof-Theory for Propositional Logic * Formal Semantics for Propositional Logic including the Truth-Tree Method * The Language of Quantificational Logic including the Theory of Descriptions. Logic is an ideal textbook for any logic student: perfect for revision, staying on top of coursework or for anyone wanting to learn about the subject. Related downloadable software for Macs and PCs is available for this title at www.logic.routledge.com.

Martin Davis on Computability, Computational Logic, and Mathematical Foundations

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Author: Eugenio G. Omodeo,Alberto Policriti

Publisher: Springer

ISBN: 3319418424

Category: Philosophy

Page: 438

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This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth problem. The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic.

Computation Theory and Logic

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Author: Egon Börger

Publisher: Springer Science & Business Media

ISBN: 9783540181705

Category: Computers

Page: 442

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In Memory of Dieter Rötting. 24.8.1937 - 4.6.1984. On the Occasion of the 50th Anniversary of His Birth

Non-commutative Multiple-Valued Logic Algebras

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Author: Lavinia Corina Ciungu

Publisher: Springer Science & Business Media

ISBN: 3319015893

Category: Mathematics

Page: 276

View: 7845

This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

Discrete Structures, Logic, and Computability

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Author: James L. Hein

Publisher: Jones & Bartlett Learning

ISBN: 0763772062

Category: Computers

Page: 1009

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Thoroughly updated, the new Third Edition of Discrete Structures, Logic, and Computability introduces beginning computer science and computer engineering students to the fundamental techniques and ideas used by computer scientists today, focusing on topics from the fields of mathematics, logic, and computer science itself. Dr. Hein provides elementary introductions to those ideas and techniques that are necessary to understand and practice the art and science of computing. The text contains all the topics for discrete structures in the reports of the IEEE/ACM Joint Task Force on Computing Curricula for computer science programs and for computer engineering programs.

Logic, Language, Information and Computation

17th International Workshop, WoLLIC 2010, Brasilia, Brazil, July 6-9, 2010, Proceedings

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Author: Anuj Dawar,Ruy de Queiroz

Publisher: Springer Science & Business Media

ISBN: 3642138233

Category: Computers

Page: 259

View: 6337

This volume contains the papers presented at WoLLIC 2010: 17th Workshop on Logic, Language, Information and Computation held during July 6–9, 2010, on the campus of Universidade de Bras ́ ?lia (UnB), Brazil. The Workshop on Logic, Language, Information and Computation (WoL- LIC) is an annual event, meeting every year since 1994, which aims at fostering interdisciplinary research in pure and applied logic. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation, and yet is small enough to allow for concrete and useful interaction among participants. The present volume contains 13 contributed papers that were selected from among 32 submissions after a rigorous review by the Program Committee. Each submission was reviewed by at least two, and on average three, Program C- mittee members. This volume also containspapersor abstractsthat relateto the seven invited talks presented at the workshop. Between them, these papers give a snapshot of some fascinating work taking place at the frontiers between computation, logic, and linguistics. We are grateful to all the people who made this meeting possible and are responsible for its success: the members of the Program Committee and the external reviewers, the invited speakers, the contributors, and the people who were involved in organizing the workshop.

Interactive Computation

The New Paradigm

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Author: Dina Goldin,Scott A. Smolka,Peter Wegner

Publisher: Springer Science & Business Media

ISBN: 3540348743

Category: Computers

Page: 487

View: 904

The interaction paradigm is a new conceptualization of computational phenomena that emphasizes interaction over algorithms, reflecting the shift in technology from main-frame number-crunching to distributed intelligent networks with graphical user interfaces. The book is arranged in four sections: "Introduction", comprising three chapters that explore and summarize the fundamentals of interactive computation; "Theory" with six chapters, each discussing a specific aspect of interaction; "Applications," five chapters showing how this principle is applied in subdisciplines of computer science; and "New Directions," presenting four multidisciplinary applications. The book challenges traditional Turing machine-based answers to fundamental questions of problem solving and the scope of computation.

Mathematical Logic

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Author: George Tourlakis

Publisher: John Wiley & Sons

ISBN: 1118030699

Category: Mathematics

Page: 294

View: 5423

A comprehensive and user-friendly guide to the use of logic inmathematical reasoning Mathematical Logic presents a comprehensive introductionto formal methods of logic and their use as a reliable tool fordeductive reasoning. With its user-friendly approach, this booksuccessfully equips readers with the key concepts and methods forformulating valid mathematical arguments that can be used touncover truths across diverse areas of study such as mathematics,computer science, and philosophy. The book develops the logical tools for writing proofs byguiding readers through both the established "Hilbert" style ofproof writing, as well as the "equational" style that is emergingin computer science and engineering applications. Chapters havebeen organized into the two topical areas of Boolean logic andpredicate logic. Techniques situated outside formal logic areapplied to illustrate and demonstrate significant facts regardingthe power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems ofPost and Gödel). Logic cannot certify all "conditional" truths, such as thosethat are specific to the Peano arithmetic. Therefore, logic hassome serious limitations, as shown through Gödel'sincompleteness theorem. Numerous examples and problem sets are provided throughout thetext, further facilitating readers' understanding of thecapabilities of logic to discover mathematical truths. In addition,an extensive appendix introduces Tarski semantics and proceeds withdetailed proofs of completeness and first incompleteness theorems,while also providing a self-contained introduction to the theory ofcomputability. With its thorough scope of coverage and accessible style,Mathematical Logic is an ideal book for courses inmathematics, computer science, and philosophy at theupper-undergraduate and graduate levels. It is also a valuablereference for researchers and practitioners who wish to learn howto use logic in their everyday work.

Computability in Context

Computation and Logic in the Real World

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Author: S. Barry Cooper

Publisher: World Scientific

ISBN: 1848162456

Category: Computers

Page: 410

View: 2745

Addresses various ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues. This book covers problems related to logic, mathematics, physical processes, real computation and learning theory.

Turing's Legacy

Developments from Turing's Ideas in Logic

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Author: Rod Downey

Publisher: Cambridge University Press

ISBN: 1107043484

Category: Computers

Page: 539

View: 1004

A collection of essays celebrating the influence of Alan Turing's work in logic, computer science and related areas.