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Extensions of CERES

  • Matthias Baaz
  • Alexander Leitsch
Chapter
Part of the Trends in Logic book series (TREN, volume 34)

Abstract

In Chapter 6 the CERES method was defined as a cut-elimination method for LK-proofs. But the method is potentially much more general and can be extended to a wide range of first-order cacluli. First of all CERES is a semantic method, in the sense that it works for all sound sequent calculi with a definable ancestor relation and a semantically complete clausal calculus. In this chapter we first show that a CERES method can be defined for virtually any sound sequent calculus. Second, we define extensions of LK by equality and definitions rules which are useful for formalizing mathematical theorems and show how to adapt CERES to these extensions of LK. The extension LKDe defined in Section 7.3 will then be used for the analysis of mathematical proofs in Section 8.5.

References

  1. 18.
    M. Baaz, A. Leitsch: Cut-Elimination and Redundancy-Elimination by Resolution. Journal of Symbolic Computation, 29, pp. 149–176, 2000.MathSciNetMATHCrossRefGoogle Scholar
  2. 20.
    M. Baaz, A. Leitsch: Towards a Clausal Analysis of Cut-Elimination. Journal of Symbolic Computation, 41, pp. 381–410, 2006.MathSciNetMATHCrossRefGoogle Scholar
  3. 29.
    P. Brauner, C. Houtmann, C. Kirchner: Principles of Superdeduction. Proceedings of LICS, pp. 41–50, 2007.Google Scholar
  4. 33.
    A. Degtyarev, A. Voronkov: Equality Reasoning in Sequent-Based Calculi. In: A. Robinson, A. Voronkov (eds.), Handbook of Automated Reasoning, vol. I,  chapter 10, Elsevier Science, Amsterdam, pp. 611–706, 2001.Google Scholar
  5. 34.
    G. Dowek, T. Hardin, C. Kirchner: Theorem Proving Modulo. Journal of Automated Reasoning, 31, pp. 32–72, 2003.MathSciNetCrossRefGoogle Scholar
  6. 35.
    G. Dowek, B. Werner: Proof Normalization Modulo. Journal of Symbolic Logic, 68(4), pp. 1289–1316, 2003.MathSciNetMATHCrossRefGoogle Scholar
  7. 36.
    E. Eder: Relative Complexities of First-Order Calculi. Vieweg, Braunschweig, 1992.MATHGoogle Scholar
  8. 38.
    G. Gentzen: Untersuchungen über das logische Schließen. Mathematische Zeitschrift, 39, pp. 405–431, 1934–1935.MathSciNetCrossRefGoogle Scholar
  9. 66.
    R. Nieuwenhuis, A. Rubio: Paramodulation-Based Theorem Proving. In: J.A. Robinson, A. Voronkov (eds.), Handbook of Automated Reasoning, Elsevier, Amsterdam, pp. 371–443, 2001.Google Scholar
  10. 74.
    G. Takeuti: Proof Theory. North-Holland, Amsterdam, 2nd edition, 1987.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

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