Resolution and the Origins of Structural Reasoning: Early Proof-Theoretic Ideas of Hertz and Gentzen (Extended Version)

Abstract

Extended version of a paper with the same title, which appeared in the Bulletin of Symbolic Logic in 2002. Abstract of the (shorter) published version: "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 propositional SLD-resolution in logic programming."