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; 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.
Table Of Contents:
I: Intuitionistic Propositional Logic.
2. Natural Deduction for Propositional Logic.
3. Negative Translation: Glivenko's Theorem.
4. Program Interpretation of Intuitionistic Logic.
5. Computations with Deductions.
6. Coherence Theorem.
7. Kripke Models.
8. Gentzen-type Propositional System LJpm.
9. Topological Completeness.
11. System LJpm.
12. Interpolation Theorem.
II: Intuitionistic Predicate Logic.
13. Natural Deduction System NJ.
14. Kripke Models for Predicate Logic.
15. Systems LJm, LJ.
16. Proof-Search in Predicate Logic.
* ISBN: 0306463946
* ISBN-13: 9780306463945
* Format: Hardcover, 144pp
* Publisher: Springer-Verlag New York, LLC
* Pub. Date: June 2008