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Natural Deduction

Author: Dag Prawitz

Publisher: Courier Dover Publications

ISBN: 9780486446554

Category: Mathematics

Page: 113

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An innovative approach to the semantics of logic, proof-theoretic semantics seeks the meaning of propositions and logical connectives within a system of inference. Gerhard Gentzen invented proof-theoretic semantics in the early 1930s, and Dag Prawitz, the author of this study, extended its analytic proofs to systems of natural deduction. Prawitz's theories form the basis of intuitionistic type theory, and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics. The concept of natural deduction follows a truly natural progression, establishing the relationship between a noteworthy systematization and the interpretation of logical signs. As this survey explains, the deduction's principles allow it to proceed in a direct fashion — a manner that permits every natural deduction's transformation into the equivalent of normal form theorem. A basic result in proof theory, the normal form theorem was established by Gentzen for the calculi of sequents. The proof of this result for systems of natural deduction is in many ways simpler and more illuminating than alternative methods. This study offers clear illustrations of the proof and numerous examples of its advantages.
Natural Deduction
Language: en
Pages: 113
Authors: Dag Prawitz
Categories: Mathematics
Type: BOOK - Published: 2006-02-24 - Publisher: Courier Dover Publications

An innovative approach to the semantics of logic, proof-theoretic semantics seeks the meaning of propositions and logical connectives within a system of inference. Gerhard Gentzen invented proof-theoretic semantics in the early 1930s, and Dag Prawitz, the author of this study, extended its analytic proofs to systems of natural deduction. Prawitz's
Advances in Natural Deduction
Language: en
Pages: 279
Authors: Luiz Carlos Pereira, Edward Haeusler, Valeria de Paiva
Categories: Philosophy
Type: BOOK - Published: 2014-07-08 - Publisher: Springer

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle
Natural Deduction
Language: en
Pages: 452
Authors: Richard T.W. Arthur
Categories: Philosophy
Type: BOOK - Published: 2011-05-25 - Publisher: Broadview Press

Richard Arthur’s Natural Deduction provides a wide-ranging introduction to logic. In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given
Natural Deduction, Hybrid Systems and Modal Logics
Language: en
Pages: 492
Authors: Andrzej Indrzejczak
Categories: Philosophy
Type: BOOK - Published: 2010-07-03 - Publisher: Springer Science & Business Media

This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic,
An Introduction to Logic - Second Edition
Language: en
Pages: 450
Authors: Richard T.W. Arthur
Categories: Philosophy
Type: BOOK - Published: 2016-11-30 - Publisher: Broadview Press

In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject,