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On the form of witness terms

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Abstract

We investigate the development of terms during cut-elimination in first-order logic and Peano arithmetic for proofs of existential formulas. The form of witness terms in cut-free proofs is characterized in terms of structured combinations of basic substitutions. Based on this result, a regular tree grammar computing witness terms is given and a class of proofs is shown to have only elementary cut-elimination.

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Authors and Affiliations

  1. Laboratoire Preuves, Programmes et Systèmes (PPS), Université Paris Diderot, 175 Rue du Chevaleret, 75013, Paris, France

    Stefan Hetzl

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  1. Stefan Hetzl
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Correspondence to Stefan Hetzl.

Additional information

This work was supported by INRIA and by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme.

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Hetzl, S. On the form of witness terms. Arch. Math. Logic 49, 529–554 (2010). https://doi.org/10.1007/s00153-010-0186-7

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