Proofs and Algorithms: An Introduction to Logic and Computability

✍ Scribed by Gilles Dowek (auth.)

• Publisher: Springer-Verlag London
• Year: 2011
• Tongue: English
• Leaves: 168
• Series: Undergraduate Topics in Computer Science
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XII
Front Matter....Pages 1-1
Predicate Logic....Pages 3-34
Models....Pages 35-52
Front Matter....Pages 53-53
Computable Functions....Pages 55-70
Computation as a Sequence of Small Steps....Pages 71-98
Front Matter....Pages 99-99
Church’s Theorem....Pages 101-115
Automated Theorem Proving....Pages 117-138
Decidable Theories....Pages 139-142
Constructivity....Pages 143-148
Epilogue....Pages 149-150
Back Matter....Pages 151-155

✦ Subjects

Theory of Computation; Mathematical Logic and Formal Languages