Sharpened lower bounds for cut elimination

We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the o...

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Bibliographic Details
Author: Buss, Samuel R.
Format: article
Publication Date:2010
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:76061
Online Access:https://ddd.uab.cat/record/76061
Access Level:Open access
Keyword:Lògica matemàtica
Demostració, Teoria de la
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Summary:We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our new lower bounds remove the constant of proportionality, giving an exponential stack of height equal to d - O(1). The proof method is based on more efficiently expressing the Gentzen-Solovay cut formulas as low depth formulas.