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Proofs and Algorithms

An Introduction to Logic and Computability

By Gilles Dowek

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This volume provides an introduction to the fundamental concepts of logic. Written for those new to the field, the text covers both elementary topics -- proofs, models, recursive functions, etc. -- as well as more advanced principles.

Full Description

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  • ISBN13: 978-0-8572-9120-2
  • 168 Pages
  • User Level: Students
  • Publication Date: January 11, 2011
  • Available eBook Formats: PDF
Full 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.
Table of Contents

Table of Contents

  1. Proofs.
  2. Predictive Logic.
  3. Models.
  4. Algorithms.
  5. Computable Functions.
  6. Computation as a Sequence of Small Steps.
  7. Proofs and Algorithms.
  8. Church's Theorem.
  9. Automated Theorem Proving.
  10. Decidable Theories.
  11. Constructivity.
  12. Epilogie.
  13. Index.
  14. Bibliography

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