A Short Introduction to Intuitionistic Logic

  • Grigori Mints
Book

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

Table of contents

  1. Front Matter
    Pages i-ix
  2. Pages 1-4
  3. Pages 7-7
  4. Pages 41-45
  5. Pages 47-52
  6. Pages 75-81
  7. Pages 83-87
  8. Pages 89-91
  9. Intuitionistic Predicate Logic

  10. Back Matter
    Pages 125-131

About this book

Introduction

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.

Keywords

algebra calculus computer computer science logic predicate logic programming proof

Authors and affiliations

  • Grigori Mints
    • 1
  1. 1.Stanford UniversityStanford

Bibliographic information

  • DOI https://doi.org/10.1007/b115304
  • Copyright Information Kluwer Academic Publishers 2000
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-306-46394-5
  • Online ISBN 978-0-306-46975-6
  • About this book
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