# Proofs and Algorithms

## An Introduction to Logic and Computability

Textbook

Part of the Undergraduate Topics in Computer Science book series (UTICS)

1. Front Matter
Pages I-XII
2. ### Proofs

1. Front Matter
Pages 1-1
2. Gilles Dowek
Pages 3-34
3. Gilles Dowek
Pages 35-52
3. ### Algorithms

1. Front Matter
Pages 53-53
2. Gilles Dowek
Pages 55-70
3. Gilles Dowek
Pages 71-98
4. ### Proofs and Algorithms

1. Front Matter
Pages 99-99
2. Gilles Dowek
Pages 101-115
3. Gilles Dowek
Pages 117-138
4. Gilles Dowek
Pages 139-142
5. Gilles Dowek
Pages 143-148
6. Gilles Dowek
Pages 149-150
5. Back Matter
Pages 151-155

### Introduction

Proofs and Algorithms: An Introduction to Logic and Computability

Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation.

Proofs and Algorithms: An Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself.

Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.

### Keywords

Algorithm Algorithmic interpretation of proofs Automated theorem proving Computability Constructivity Cut elimination Decidability Lambda-calculus Natural deduction Proof Rewriting Sequent calculus Turing Machines

#### Authors and affiliations

1. 1.Labo. d'InformatiqueÉcole PolytechniquePalaiseau CXFrance

Gilles Dowek is a Professor at École Polytechnique. He is also a Researcher at the Laboratoire d'Informatique de l'École Polytechnique and the Institut National de Recherche en Informatique et en Automatique (INRIA). His research concerns the formalization of mathematics and the mechanization of reasoning. His main contribution is a reformulation of the axiomatic method which provides a central role to the notion of computation.

### Bibliographic information

• Book Title Proofs and Algorithms
• Book Subtitle An Introduction to Logic and Computability
• Authors Gilles Dowek
• Series Title Undergraduate Topics in Computer Science
• DOI https://doi.org/10.1007/978-0-85729-121-9
• Copyright Information Springer-Verlag London Limited 2011
• Publisher Name Springer, London
• eBook Packages Computer Science Computer Science (R0)
• Softcover ISBN 978-0-85729-120-2
• eBook ISBN 978-0-85729-121-9
• Series ISSN 1863-7310
• Edition Number 1
• Number of Pages XII, 156
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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