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AuthorMints, Grigori. author
TitleA Short Introduction to Intuitionistic Logic [electronic resource] / by Grigori Mints
ImprintBoston, MA : Springer US, 2000
Connect tohttp://dx.doi.org/10.1007/b115304
Descript IX, 131 p. online resource

SUMMARY

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


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: Glivenkoโ{128}{153}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


Mathematics Logic Computer science -- Mathematics Mathematical logic Mathematics Mathematical Logic and Foundations Logic Mathematics of Computing



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