A Short Introduction to Intuitionistic Logic

Grigori Mints

ISBN 10: 0306463946 / ISBN 13: 9780306463945

Published by Springer Science+Business Media, US, 2000

About this Item

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 tchniques are presented first for propositional logic, then part II inroduces extensions to predicate logic. This material provides an introduction and a 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 and 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; lagebraic and topological semantics; proof-search methods; and interpolation theorem.

Seller Inventory # LU-9780306463945

Bibliographic Details

• Title: A Short Introduction to Intuitionistic Logic
• Publisher: Springer Science+Business Media, US
• Publication Date: 2000
• Language: English
• ISBN 10: 0306463946
• ISBN 13: 9780306463945
• Binding: Hardback
• Edition: 2000 ed.
• Condition: New

About this title

Synopsis

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.

Review

`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