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A Short Introduction to Intuitionistic Logic

  • Book
  • © 2000

Overview

Authors:
  1. Grigori Mints

    1. Stanford University, Stanford

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Part of the book series: University Series in Mathematics (USMA)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    Pages 1-4

  3. Preliminaries

    Pages 7-7

  4. Natural Deduction for Propositional Logic

    Pages 9-22

  5. Negative Translation: Glivenko’s Theorem

    Pages 23-24

  6. Program Interpretation of Intuitionistic Logic

    Pages 25-30

  7. Computations with Deductions

    Pages 31-39

  8. Coherence Theorem

    Pages 41-45

  9. Kripke Models

    Pages 47-52

  10. Gentzen-type Propositional System LJpm

    Pages 53-68

  11. Topological Completeness

    Pages 69-74

  12. Proof-search

    Pages 75-81

  13. System LJp

    Pages 83-87

  14. Interpolation Theorem

    Pages 89-91

  15. Intuitionistic Predicate Logic

    1. Natural Deduction System NJ

      Pages 95-104

    2. Kripke Models for Predicate Logic

      Pages 105-108

    3. Systems LJm, LJ

      Pages 109-118

    4. Proof-Search in Predicate Logic

      Pages 119-124

  16. Back Matter

    Pages 125-131
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Keywords

About this book

Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this book short was inventing new proofs of several theorems. The presentation is based on natural deduction. The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed from materal for several courses taught at Stanford University in 1992-1999.

Reviews

`This is the most welcome addition to the literature on intuitionistic logic, providing a substantial reference of value comparable to that of better established references for classical mathematical logic. The development of Mints' book is natural, elegant and accessible, with a minimum of fuss but no lack of attention to important detail.
Overall, the book is an excellent addition to the literature.'
Mathematical Reviews, 2002b

Authors and Affiliations

  • Stanford University, Stanford

    Grigori Mints

Bibliographic Information

  • Book Title: A Short Introduction to Intuitionistic Logic

  • Authors: Grigori Mints

  • Series Title: University Series in Mathematics

  • DOI: https://doi.org/10.1007/b115304

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2000

  • Hardcover ISBN: 978-0-306-46394-5Published: 31 October 2000

  • Softcover ISBN: 978-1-4757-7319-4Published: 26 April 2013

  • eBook ISBN: 978-0-306-46975-6Published: 20 December 2005

  • Edition Number: 1

  • Number of Pages: IX, 131

  • Topics: Mathematical Logic and Foundations, Logic, Mathematics of Computing

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