Structural Proof Theory

A concise introduction to structural proof theory, a branch of logic studying the general structure of logical and mathematical proofs.

Sara Negri (Author), Jan von Plato (Author), Aarne Ranta (Appendix by)

9780521793070, Cambridge University Press

Hardback, published 18 June 2001

276 pages
23.5 x 16 x 2.1 cm, 0.599 kg

"....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

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.

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.

Subject Areas: Philosophy of science [PDA], Mathematics [PB], Philosophy: logic [HPL]