Proofs and Algorithms: An Introduction to Logic and Computability (Undergraduate Topics in Computer Science) 2011th Edition by Gilles Dowek (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review 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) From the Back Cover Proofs and Algorithms: An Introduction to Logic and ComputabilityLogic 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. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There are a lot of “intermediate” logic textbooks out there, some of them even written by titans like Kleene; however, the reader who was not already fully primed to assimilate highly abstract proofs will usually be frustrated by their high dudgeon concerning breaking things down. Gilles Dowek has written a metalogic text that actually begins with the knowledge-base of today’s logic learner and elegantly provides a comprehensible way to understand the most major results of modern logic. Though the book is quite concise, Dowek manages to explain completeness and incompleteness, decidability and undecidability, and even a few more select items like cut elimination in his 150 pages; if you have the level of “mathematical maturity” provided by an introductory class in discrete mathematics you will be able to easily follow his exposition. The treatment of computability will appeal to more practically-minded CS students; using a cool trick general recursive functions, “productions”, the lambda calculus (usually absent in similar texts) and Turing machines are all exhibited and shown to be equivalent.Though some of the symbolic machinery points forward to texts in advanced pure logic, much of the material will benefit a humble “coder”. A good place to start.

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