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Sequent calculus and complexity theory

  • Duccio Pianigiani

We come to a formalism introduced by Gentzen, namely the sequents calculus. We introduce here the basic concepts and prove the most important result about it, namely cut-elimination. Actually we will not illustrate here the cut elimination for pure logic, but rather a proof of the free-cut elimination theorem, according to which some cuts can be Eliminated, in fact the only results available for theories (i.e. logic plus proper axioms and induction rule), since we will see that for them the full cut-elimination is not valid. We show how this result has been applied for the characterization of functions computable in polynomial time.

  • Keywords:
  • Sequent calculus,
  • cut-elimination,
  • free-cut elimination,
  • provably total functions,
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Duccio Pianigiani

University of Siena, Italy - ORCID: 0000-0001-9441-7226

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  • Publication Year: 2025
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  • Publication Year: 2025

Chapter Information

Chapter Title

Sequent calculus and complexity theory

Authors

Duccio Pianigiani

Language

English

DOI

10.36253/979-12-215-0778-2.12

Peer Reviewed

Publication Year

2025

Copyright Information

© 2025 Author(s)

Content License

CC BY-SA 4.0

Metadata License

CC0 1.0

Bibliographic Information

Book Title

Lectures in Proof Theory and Complexity

Authors

Duccio Pianigiani

Peer Reviewed

Publication Year

2025

Copyright Information

© 2025 Author(s)

Content License

CC BY-SA 4.0

Metadata License

CC0 1.0

Publisher Name

Firenze University Press, USiena Press

DOI

10.36253/979-12-215-0778-2

eISBN (pdf)

979-12-215-0778-2

eISBN (xml)

979-12-215-0779-9

Series Title

UNIverSI. Ricerca e Didattica all’Università di Siena

Series ISSN

3035-5915

Series E-ISSN

3035-5931

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