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.
University of Siena, Italy - ORCID: 0000-0001-9441-7226
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
Metadata License
Book Title
Lectures in Proof Theory and Complexity
Authors
Duccio Pianigiani
Peer Reviewed
Publication Year
2025
Copyright Information
© 2025 Author(s)
Content License
Metadata License
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