A Short Introduction to Intuitionistic Logic
Published on 20. December 2005
IX, 131 pages
978-0-306-46975-6 (ISBN)
Description
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 / Votes
` 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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Other editions
Additional editions
Grigori Mints
A Short Introduction to Intuitionistic Logic
Book
04/2013
Springer
€160.49
Shipment within 15-20 days
Grigori Mints
A Short Introduction to Intuitionistic Logic
Book
10/2000
Plenum Publishing Co.,N.Y.
€149.79
Shipment within 10-15 days
Content
Intuitionistic Predicate Logic.- Natural Deduction System NJ.- Kripke Models for Predicate Logic.- Systems LJm, LJ.- Proof-Search in Predicate 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 LJp.- Interpolation Theorem.
