A Short Introduction to Intuitionistic Logic

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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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.

• algebra
• calculus
• computer
• computer science
• logic
• predicate logic
• programming
• proof

`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

• Stanford University, Stanford

  Grigori Mints

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