Related Research

Part of the Trends in Logic book series (TREN, volume 34)


Proof transformations for the analysis of proofs can roughly be classified according to the degree to which they eliminate the structure of the given proof.


  1. 1.
    M. Aigner, G.M. Ziegler: Proofs from THE BOOK. Springer, Berlin, 1998.MATHGoogle Scholar
  2. 2.
    P.B. Andrews: Resolution in Type Theory. Journal of Symbolic Logic, 36, pp. 414–432, 1971.MathSciNetMATHCrossRefGoogle Scholar
  3. 14.
    M. Baaz, R. Iemhoff: The Skolemization of Existential Quantifiers in Intuitionistic Logic. Annals of Pure and Applied Logic, 142, pp. 269–295, 2006.MathSciNetMATHCrossRefGoogle Scholar
  4. 32.
    Coq: Project Home Page. URL:
  5. 39.
    P. Gerhardy, U. Kohlenbach: Extracting Herbrand Disjunctions by Functional Interpretations. Archive for Mathematical Logic, 44, pp. 633–644, 2005.MathSciNetMATHCrossRefGoogle Scholar
  6. 45.
    S. Hetzl: Proof Profiles, Characteristic Clause Sets and Proof Transformations. PhD Thesis, Vienna University of Technology, 2007.Google Scholar
  7. 46.
    S. Hetzl, A. Leitsch: Proof Transformations and Structural Invariance. In Algebraic and Proof Theoretic Aspects of Non-classical Logics. Lecture Notes in Computer Science, 4460, pp. 201–230, 2007.Google Scholar
  8. 49.
    S. Hetzl, A. Leitsch, D. Weller, B. Woltzenlogel Paleo: A Clausal Approach to Proof Analysis in Second-Order Logic. Proceedings of the LFCS 2009, Lecture Notes in Computer Science, 5407, pp. 214–229, 2009.Google Scholar
  9. 52.
    Isabelle: System Home Page. URL: Research/HVG/Isabelle.
  10. 54.
    U. Kohlenbach: Applied Proof Theory: Proof Interpretations and their Use in Mathematics. In Springer Monographs in Mathematics, Springer, Berlin, 2009.Google Scholar
  11. 56.
    G. Kreisel: On the Interpretation of Nonfinitist Proofs, Part I. Journal of Symbolic Logic 16, pp. 241–267, 1951.MathSciNetMATHCrossRefGoogle Scholar
  12. 58.
    G. Kreisel: Mathematical Significance of Consistency Proofs. Journal of Symbolic Logic, 23, pp. 155–182, 1958.MathSciNetCrossRefGoogle Scholar
  13. 61.
    A. Leitsch: The Resolution Calculus. EATCS Texts in Theoretical Computer Science. Springer, Berlin, 1997.Google Scholar
  14. 63.
    H. Luckhardt: Herbrand-Analysen zweier Beweise des Satzes von Roth: polynomiale Anzahlschranken. Journal of Symbolic Logic, 54, pp. 234–263, 1989.MathSciNetMATHCrossRefGoogle Scholar
  15. 80.
    B. Woltzenlogel Paleo: A General Analysis of Cut-Elimination by CERes. PhD Thesis, Vienna University of Technology, 2009.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Vienna University of TechnologyViennaAustria
  2. 2.Vienna University of TechnologyViennaAustria

Personalised recommendations