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Unwinding a Non-effective Cut Elimination Proof

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Computer Science – Theory and Applications (CSR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3967))

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Abstract

Non-effective cut elimination proof uses Koenig’s lemma to obtain a non-closed branch of a proof-search tree τ (without cut) for a first order formula A, if A is not cut free provable. A partial model (semi-valuation) corresponding to this branch and verifying ¬A is extended to a total model for ¬A using arithmetical comprehension. This contradicts soundness, if A is derivable with cut. Hence τ is a cut free proof of A. The same argument works for Herbrand Theorem. We discuss algorithms of obtaining cut free proofs corresponding to this schema and quite different from complete search through all possible proofs.

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Author information

Authors and Affiliations

  1. Stanford University, Stanford, Ca, 94305, USA

    Grigori Mints

Authors
  1. Grigori Mints
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Editors and Affiliations

  1. IRMAR, Université de Rennes, Campus de Beaulieu, 35042, Rennes Cedex, France

    Dima Grigoriev

  2. Intel Corporation, JF1-13, 2111 NE 25th Avenue, 97124, Hillsboro, OR, USA

    John Harrison

  3. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, St., 191023, Petersburg, Russia

    Edward A. Hirsch

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© 2006 Springer-Verlag Berlin Heidelberg

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Mints, G. (2006). Unwinding a Non-effective Cut Elimination Proof. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_27

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  • DOI: https://doi.org/10.1007/11753728_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34166-6

  • Online ISBN: 978-3-540-34168-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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