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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| 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 |
| 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. |
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