National Science Library of Georgia

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Structural proof theory / Sara Negri, Jan von Plato ; with an appendix by Aarne Ranta.

By: Contributor(s): Material type: TextTextPublisher: Cambridge : Cambridge University Press, 2001Description: 1 online resource (xvii, 257 pages) : digital, PDF file(s)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780511527340 (ebook)
Subject(s): Additional physical formats: Print version: : No titleDDC classification:
  • 511.3 21
LOC classification:
  • QA9.54 .N44 2001
Online resources:
Contents:
1. From natural deduction to sequent calculus -- 2. Sequent calculus for intuitionistic 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 -- App. A. Simple type theory and categorical grammar -- App. B. Proof theory and constructive type theory -- App. C. PESCA -- A proof editor for sequent calculus / Aarne Ranta.
Summary: 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.
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Title from publisher's bibliographic system (viewed on 05 Oct 2015).

1. From natural deduction to sequent calculus -- 2. Sequent calculus for intuitionistic 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 -- App. A. Simple type theory and categorical grammar -- App. B. Proof theory and constructive type theory -- App. C. PESCA -- A proof editor for sequent calculus / Aarne Ranta.

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.

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