Structural Proof Theory

Sara Negri (University of Helsinki), Jan von Plato (University of Helsinki), Aarne Ranta

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English

Cambridge University Press
05 August 2008

Philosophy: logic; Mathematics & Sciences; Mathematical logic; Philosophy of science

Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.

By: Sara Negri (University of Helsinki), Jan von Plato (University of Helsinki)
Appendix by: Aarne Ranta
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm, Spine: 16mm
Weight: 410g
ISBN: 9780521068420
ISBN 10: 0521068428
Pages: 276
Publication Date: 05 August 2008
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Introduction; 1. From natural deduction to sequent calculus; 2. Sequent calculus for institutionistic logic; 3. Sequent calculus for classical logic; 4. The quantifiers; 5. Variants of sequent calculi; 6. Structural proof analysis of axiomatic theories; 7. Intermediate logical systems; 8. Back to natural deduction; Conclusion: diversity and unity in structural proof theory; Appendix A. Simple type theory and categorical grammar; Appendix B. Proof theory and constructive type theory; Appendix C. A proof editor for sequent calculus.

Reviews for Structural Proof Theory

"""...The book makes significant original contributions while remaining accessible to the logician/philosopher/mathematician who wants to learn elementary proof theory..."" Aldo Antonelli, University of California, Irvine"