Overview
- Covers elementary topics - proofs, models, recursive functions, Church's theorem
- Contains an introduction to more advanced topics - rewriting, lambada-calculus, sequent calculus, automated theorem proving
- This book is written for students who have had no exposure to logic before
- Includes supplementary material: sn.pub/extras
Part of the book series: Undergraduate Topics in Computer Science (UTICS)
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Table of contents (9 chapters)
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Front Matter
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Proofs
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Front Matter
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Algorithms
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Front Matter
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Proofs and Algorithms
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Front Matter
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Back Matter
Keywords
About this book
Proofs and Algorithms: 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.
Reviews
From the reviews:
“This work examines when the application of an algorithm can replace the construction of a proof. … focuses on establishing that provability is undecidable in predicate logic (Church’s theorem). The text generally consists of propositions followed by proofs, with commentary, examples, and exercises interspersed. … The book would be of interest to those with adequate background. Summing Up: Recommended. Graduate students and above.” (J. R. Burke, Choice, Vol. 49 (1), September, 2011)
“Mathematical logic is a challenging subject for many students. … this book, with its focus on the nature of proofs and algorithms and their relationship, appears to be targeted precisely for such an audience and should appeal to computer scientists and philosophers … . this book remains an introductory book on mathematical logic suited for a beginning graduate course in logic. … Its conciseness makes it well suited for a one-semester graduate course.” (Burkhard Englert, ACM Computing Reviews, February, 2012)
Authors and Affiliations
About the author
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
Publisher: Springer London
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer-Verlag London Limited 2011
Softcover ISBN: 978-0-85729-120-2Published: 14 January 2011
eBook ISBN: 978-0-85729-121-9Published: 11 January 2011
Series ISSN: 1863-7310
Series E-ISSN: 2197-1781
Edition Number: 1
Number of Pages: XII, 156
Topics: Theory of Computation, Mathematical Logic and Formal Languages