A short introduction to intuitionistic logic / Grigori Mints.

Format:

Book

Author/Creator:

Mint︠s︡, G. E.

Series:

University series in mathematics (Plenum Press)

University series in mathematics

Language:

English

Subjects (All):

Intuitionistic mathematics.

Physical Description:

1 online resource (142 p.)

Edition:

1st ed. 2000.

Place of Publication:

New York : Kluwer Academic / Plenum Publishers, 2000.

Language Note:

English

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.

Contents:

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.

Notes:

Description based upon print version of record.

Description based on publisher supplied metadata and other sources.

Includes bibliographical references and index.

ISBN:

1-280-20550-4

9786610205509

0-306-46975-8

OCLC:

52085722