Bulletin of Symbolic Logic

Resolution and the Origins of Structural Reasoning: Early Proof-Theoretic Ideas of Hertz and Gentzen

Peter Schroeder-Heister

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Abstract

In the 1920s, Paul Hertz (1881-1940) developed certain calculi based on structural rules only and established normal form results for proofs. It is shown that he anticipated important techniques and results of general proof theory as well as of resolution theory, if the latter is regarded as a part of structural proof theory. Furthermore, it is shown that Gentzen, in his first paper of 1933, which heavily draws on Hertz, proves a normal form result which corresponds to the completeness of prepositional SLD-resolution in logic programming.

Article information

Source
Bull. Symbolic Logic, Volume 8, Number 2 (2002), 246-265.

Dates
First available in Project Euclid: 20 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1182353872

Digital Object Identifier
doi:10.2178/bsl/1182353872

Mathematical Reviews number (MathSciNet)
MR1919590

Zentralblatt MATH identifier
1005.03004

JSTOR
links.jstor.org

Citation

Schroeder-Heister, Peter. Resolution and the Origins of Structural Reasoning: Early Proof-Theoretic Ideas of Hertz and Gentzen. Bull. Symbolic Logic 8 (2002), no. 2, 246--265. doi:10.2178/bsl/1182353872. https://projecteuclid.org/euclid.bsl/1182353872


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