Proof transformation by CERES

Authors:
Matthias Baaz;Stefan Hetzl;Alexander Leitsch;Clemens Richter;Hendrik Spohr
Affiliations:
Institute of Discrete Mathematics and Geometry (E104), Vienna University of Technology, Vienna, Austria;Institute of Computer Languages (E185), Vienna University of Technology, Vienna, Austria;Institute of Computer Languages (E185), Vienna University of Technology, Vienna, Austria;Institute of Computer Languages (E185), Vienna University of Technology, Vienna, Austria;Institute of Computer Languages (E185), Vienna University of Technology, Vienna, Austria
Venue:
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
Year:
2006

Citing 4
Cited 4

Relative complexities of first order calculi

Relative complexities of first order calculi
Cut-elimination and redundancy-elimination by resolution

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CERES: An analysis of Fürstenberg's proof of the infinity of primes

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A Clausal Approach to Proof Analysis in Second-Order Logic

LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
System description: the proof transformation system CERES

IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning

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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.