Journal of Symbolic Logic

On the non-confluence of cut-elimination

Matthias Baaz and Stefan Hetzl

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We study cut-elimination in first-order classical logic. We construct a sequence of polynomial-length proofs having a non-elementary number of different cut-free normal forms. These normal forms are different in a strong sense: they not only represent different Herbrand-disjunctions but also differ in their propositional structure.

This result illustrates that the constructive content of a proof in classical logic is not uniquely determined but rather depends on the chosen method for extracting it.

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J. Symbolic Logic, Volume 76, Issue 1 (2011), 313-340.

First available in Project Euclid: 4 January 2011

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Baaz, Matthias; Hetzl, Stefan. On the non-confluence of cut-elimination. J. Symbolic Logic 76 (2011), no. 1, 313--340. doi:10.2178/jsl/1294171002.

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