Herbrand Sequent Extraction

Authors:
Stefan Hetzl;Alexander Leitsch;Daniel Weller;Bruno Woltzenlogel Paleo
Affiliations:
Institute of Computer Languages (E185), Vienna University of Technology, Vienna, Austria 1040;Institute of Computer Languages (E185), Vienna University of Technology, Vienna, Austria 1040;Institute of Computer Languages (E185), Vienna University of Technology, Vienna, Austria 1040;Institute of Computer Languages (E185), Vienna University of Technology, Vienna, Austria 1040
Venue:
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Year:
2008

Citing 6
Cited 4

Cut-elimination and redundancy-elimination by resolution

Journal of Symbolic Computation - Special issue on advances in first-order theorem proving
On Herbrand's Theorem

LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
The state of CASC

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

Theoretical Computer Science
Proof transformations and structural invariance

Algebraic and proof-theoretic aspects of non-classical logics
Proof transformation by CERES

MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management

Atomic cut introduction by resolution: proof structuring and compression

LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
System description: the proof transformation system CERES

IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Towards algorithmic cut-introduction

LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Proof Nets for Herbrand’s Theorem

ACM Transactions on Computational Logic (TOCL)

Quantified Score

Hi-index	0.00

Visualization

Abstract

Computer generated proofs of interesting mathematical theorems are usually too large and full of trivial structural information, and hence hard to understand for humans. Techniques to extract specific essential information from these proofs are needed. In this paper we describe an algorithm to extract Herbrand sequents from proofs written in Gentzen's sequent calculus LKfor classical first-order logic. The extracted Herbrand sequent summarizes the creative information of the formal proof, which lies in the instantiations chosen for the quantifiers, and can be used to facilitate its analysis by humans. Furthermore, we also demonstrate the usage of the algorithm in the analysis of a proof of the equivalence of two different definitions for the mathematical concept of lattice, obtained with the proof transformation system CERES.