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THE ELIMINATION OF ATOMIC CUTS AND THE SEMISHORTENING PROPERTY FOR GENTZEN’S SEQUENT CALCULUS WITH EQUALITY

Part of: Proof theory and constructive mathematics

Published online by Cambridge University Press:  13 August 2019

FRANCO PARLAMENTO  and
FLAVIO PREVIALE
FRANCO PARLAMENTO
Affiliation:
DEPARTMENT OF MATHEMATICS, COMPUTER SCIENCE AND PHYSICS UNIVERSITY OF UDINE VIA DELLE SCIENZE 206, 33100UDINE, ITALYE-mail: [email protected]
FLAVIO PREVIALE
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF TURIN VIA CARLO ALBERTO 10, 10123TORINO, ITALYE-mail: [email protected]
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Abstract

We study various extensions of Gentzen’s sequent calculus obtained by adding rules for equality. One of them is singled out as particularly natural and shown to satisfy full cut elimination, namely, also atomic cuts can be eliminated. Furthermore we tell apart the extensions that satisfy full cut elimination from those that do not and establish a strengthened form of the nonlenghtening property of Lifschitz and Orevkov.

Keywords

sequent calculuscut eliminationequality rules

MSC classification

Primary: 03F05: Cut-elimination and normal-form theorems
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 4 , December 2021 , pp. 813 - 837
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Copyright
© Association for Symbolic Logic 2019

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