A Short Introduction to Intuitionistic Logic

By: Grigori Mints

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Hardcover | 31 October 2000

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144 Pages

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24.13 x 15.88 x 2.54

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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.

Industry 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

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Introduction
Intuitionistic Propositional Logic
Preliminaries
Natural Deduction for Propositional Logic
Negative Translation: Glivenko's Theorem
Program Interpretation of Intuitionistic Logic
Computations with Deductions
Coherence Theorem
Kripke Models
Gentzen-type Propositional System LJpm
Topological Completeness
Proof-Search
System LJpm
Interpolation Theorem
Intuitionistic Predicate Logic
Natural Deduction System NJ
Kripke Models for Predicate Logic
Systems LJm, LJ
Proof-Search in Predicate Logic
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

A Short Introduction to Intuitionistic Logic

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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