A Short Introduction to Intuitionistic Logic (University Series in Mathematics) (University Series in Mathematics)

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. "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 intutionistic 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, and interpolation theorem. The text developed from material for several courses taught at Stanford University in 1992-1999."--BOOK JACKET. Introduction....Pages 1-4 Preliminaries....Pages 7-7 Natural Deduction for Propositional Logic....Pages 9-22 Negative Translation: Glivenko’s Theorem....Pages 23-24 Program Interpretation of Intuitionistic Logic....Pages 25-30 Computations with Deductions....Pages 31-39 Coherence Theorem....Pages 41-45 Kripke Models....Pages 47-52 Gentzen-type Propositional System LJpm....Pages 53-68 Topological Completeness....Pages 69-74 Proof-search....Pages 75-81 System LJp....Pages 83-87 Interpolation Theorem....Pages 89-91 Natural Deduction System NJ....Pages 95-104 Kripke Models for Predicate Logic....Pages 105-108 Systems LJm, LJ....Pages 109-118 Proof-Search in Predicate Logic....Pages 119-124 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. The presentation is based on natural deduction and readers are assumed to be familiar with basic notions of first order logic Intuitionistic logic is studied here as part of familiar classical logic which allows an effective interpretation and mechanical extraction of programs from proofs.