Computability and Logic


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

Publisher: Cambridge University Press

ISBN: 9780521007580

Category: Philosophy

Page: 356

View: 9799

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


Author: George Boolos,Richard C. Jeffrey

Publisher: CUP Archive

ISBN: 9780521204026

Category: Computable functions

Page: 262

View: 2406

Combinatorics, Computability and Logic

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


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

Publisher: Springer Science & Business Media

ISBN: 1447107179

Category: Mathematics

Page: 251

View: 484

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.

Berechenbarkeit, Komplexität, Logik

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


Author: Egon Börger

Publisher: Springer-Verlag

ISBN: 3322877779

Category: Computers

Page: 470

View: 9437

Elementary Logic

For Software Development


Author: Robert Lover

Publisher: Springer Science & Business Media

ISBN: 9781848000827

Category: Computers

Page: 314

View: 1679

The ability to reason correctly is critical to most aspects of computer science and to software development in particular. This book teaches readers how to better reason about software development, to communicate reasoning, to distinguish between good and bad reasoning, and to read professional literature that presumes knowledge of elementary logic. The reader’s knowledge and understanding can be assessed through numerous examples and exercises. This book provides a reader-friendly foundation to logic and offers valuable insight into the topic, thereby serving as a helpful reference for practitioners, as well as students studying software development.

Computability in Context

Computation and Logic in the Real World


Author: S. Barry Cooper

Publisher: World Scientific

ISBN: 1848162456

Category: Computers

Page: 410

View: 8338

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.

Models and Computability


Author: S. Barry Cooper,John K. Truss

Publisher: Cambridge University Press

ISBN: 9780521635509

Category: Mathematics

Page: 419

View: 5825

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

Discrete Structures, Logic, and Computability


Author: James L. Hein

Publisher: Jones & Bartlett Learning

ISBN: 0763772062

Category: Computers

Page: 1009

View: 2307

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.

Computation and Logic in the Real World

Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007, Proceedings


Author: S. Barry Cooper,Benedikt Lowe

Publisher: Springer Science & Business Media

ISBN: 9783540730002

Category: Computers

Page: 826

View: 2805

CiE2007:ComputationandLogicintheRealWorld Siena,Italy,June18-23,2007 Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical devel- ment, and applications. Among the aims of the network is to advance our t- oretical understanding of what can and cannot be computed, by any means of computation. Its scienti'c vision is broad: computations may be performed with discrete or continuous data by all kinds of algorithms, programs, and - chines. Computations may be made by experimenting with any sort of physical system obeying the laws of a physical theory such as Newtonian mechanics, quantum theory, or relativity. Computations may be very general, depending upon the foundations of set theory; or very speci'c, using the combinatorics of ?nite structures. CiE also works on subjects intimately related to computation, especially theories of data and information, and methods for formal reasoning about computations. The sources of new ideas and methods include practical developments in areas such as neural networks, quantum computation, natural computation, molecular computation, computational learning. Applications are everywhere,especially, in algebra,analysisand geometry, or data types and p- gramming. Within CiE there is general recognition of the underlying relevance of computability to physics and a broad range of other sciences, providing as it does a basic analysis of the causal structure of dynamical systems.


Rekursive und Programmierbare Funktionen


Author: Walter Felscher

Publisher: Springer-Verlag

ISBN: 3642780199

Category: Computers

Page: 478

View: 5279

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.



Author: Paul Tomassi

Publisher: Routledge

ISBN: 1134705913

Category: Philosophy

Page: 432

View: 8938

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

Mathematical Logic


Author: George Tourlakis

Publisher: John Wiley & Sons

ISBN: 1118030699

Category: Mathematics

Page: 294

View: 836

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.

Logic, Language, Information and Computation

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


Author: Anuj Dawar,Ruy de Queiroz

Publisher: Springer Science & Business Media

ISBN: 3642138233

Category: Computers

Page: 259

View: 8827

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.

A Science of Operations

Machines, Logic and the Invention of Programming


Author: Mark Priestley

Publisher: Springer Science & Business Media

ISBN: 9781848825550

Category: Computers

Page: 342

View: 3228

Today, computers fulfil a dazzling array of roles, a flexibility resulting from the great range of programs that can be run on them. A Science of Operations examines the history of what we now call programming, defined not simply as computer programming, but more broadly as the definition of the steps involved in computations and other information-processing activities. This unique perspective highlights how the history of programming is distinct from the history of the computer, despite the close relationship between the two in the 20th century. The book also discusses how the development of programming languages is related to disparate fields which attempted to give a mechanical account of language on the one hand, and a linguistic account of machines on the other. Topics and features: Covers the early development of automatic computing, including Babbage’s “mechanical calculating engines” and the applications of punched-card technology, examines the theoretical work of mathematical logicians such as Kleene, Church, Post and Turing, and the machines built by Zuse and Aiken in the 1930s and 1940s, discusses the role that logic played in the development of the stored program computer, describes the “standard model” of machine-code programming popularised by Maurice Wilkes, presents the complete table for the universal Turing machine in the Appendices, investigates the rise of the initiatives aimed at developing higher-level programming nota tions, and how these came to be thought of as ‘languages’ that could be studied independently of a machine, examines the importance of the Algol 60 language, and the framework it provided for studying the design of programming languages and the process of software development and explores the early development of object-oriented languages, with a focus on the Smalltalk project. This fascinating text offers a new viewpoint for historians of science and technology, as well as for the general reader. The historical narrative builds the story in a clear and logical fashion, roughly following chronological order.

Turing's Legacy

Developments from Turing's Ideas in Logic


Author: Rod Downey

Publisher: Cambridge University Press

ISBN: 1107043484

Category: Computers

Page: 539

View: 4190

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

Computability and Models

Perspectives East and West


Author: Barry S. Cooper,Sergei S. Goncharov

Publisher: Springer Science & Business Media

ISBN: 9780306474002

Category: Computers

Page: 375

View: 9411

There are few notions as fundamental to contemporary science as those of computability and modelling. Computability and Models attempts to make some of the exciting and important new research developments in this area accessible to a wider readership. Written by international leaders drawn from major research centres both East and West, this book is an essential addition to scientific libraries serving both specialist and the interested non-specialist reader.

The Philosophy of Mathematics Today


Author: Matthias Schirn

Publisher: Oxford University Press

ISBN: 9780199262625

Category: Philosophy

Page: 638

View: 1677

The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come.