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Proof Transformation by CERES

  • Matthias Baaz
  • Stefan Hetzl
  • Alexander Leitsch
  • Clemens Richter
  • Hendrik Spohr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4108)

Abstract

Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by constructing a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton of an LK-proof with only atomic cuts.

In this paper we present an extension of CERES to a calculus LKDe which is stronger than the Gentzen calculus LK (it contains rules for introduction of definitions and equality rules). This extension makes it much easier to formalize mathematical proofs and increases the performance of the cut-elimination method. The system CERES already proved efficient in handling very large proofs.

Keywords

Theorem Prove Mathematical Proof Proof Theory Equality Rule Unary Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Matthias Baaz
    • 1
  • Stefan Hetzl
    • 2
  • Alexander Leitsch
    • 2
  • Clemens Richter
    • 2
  • Hendrik Spohr
    • 2
  1. 1.Institute of Discrete Mathematics and Geometry (E104)Vienna University of TechnologyViennaAustria
  2. 2.Institute of Computer Languages (E185)Vienna University of TechnologyViennaAustria

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