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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: 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.
List of contents
Proofs.-Predictive Logic.-Models.-Algorithms.-Computable Functions.-Computation as a Sequence of Small Steps.-Proofs and Algorithms.-Church's Theorem.-Automated Theorem Proving.-Decidable Theories.-Constructivity.-Epilogie.-Index.-Bibliography
About the author
Gilles Dowek is Director of Research at INRIA and heads the LOGICAL project-team. He is also a Professor at the École Polytechnique and a researcher at the École Polytechnique's Computer Science Laboratory (LIX). He is an advisor to the National Institute of Aerospace, a NASA Langley research centre laboratory. His research focuses on formalising mathematics, on demonstration processing systems related to quantum programming language design and on safety for aerospace systems. He has written several works aimed at explaining maths and science theory in layman's terms.
Summary
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: 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.
Report
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)
