A Short Introduction to Intuitionistic Logic

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.