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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Detalles Bibliográficos
Autor: Buss, Samuel R.
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:76061
Acceso en línea:https://ddd.uab.cat/record/76061
Access Level:acceso abierto
Palabra clave:Lògica matemàtica
Demostració, Teoria de la
Descripción
Sumario: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.