Lectures on Jacques Herbrand as a Logician. Wirth, C., Siekmann, J., Benzmüller, C., & Autexier, S. SEKI Publications (ISSN 1437-4447), 2009. arXiv:0902.4682doi abstract bibtex We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides the well-known correction of Herbrand's False Lemma by Goedel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its consequences on Herbrand's Modus Ponens Elimination. Besides Herbrand's Fundamental Theorem and its relation to the Loewenheim-Skolem-Theorem, we carefully investigate Herbrand's notion of intuitionism in connection with his notion of falsehood in an infinite domain. We sketch Herbrand's two proofs of the consistency of arithmetic and his notion of a recursive function, and last but not least, present the correct original text of his unification algorithm with a new translation.
@book{R43,
Abstract = {We give some lectures on the work on formal logic of
Jacques Herbrand, and sketch his life and his
influence on automated theorem proving. The intended
audience ranges from students interested in logic
over historians to logicians. Besides the well-known
correction of Herbrand's False Lemma by Goedel and
Dreben, we also present the hardly known unpublished
correction of Heijenoort and its consequences on
Herbrand's Modus Ponens Elimination. Besides
Herbrand's Fundamental Theorem and its relation to
the Loewenheim-Skolem-Theorem, we carefully
investigate Herbrand's notion of intuitionism in
connection with his notion of falsehood in an
infinite domain. We sketch Herbrand's two proofs of
the consistency of arithmetic and his notion of a
recursive function, and last but not least, present
the correct original text of his unification
algorithm with a new translation.},
Author = {Wirth, Claus-Peter and Siekmann, J{\"o}rg and
Benzm{\"u}ller, Christoph and Autexier, Serge},
Keywords = {own, Jacques Herbrand, History of Logic},
Note = {arXiv:0902.4682},
Publisher = {SEKI Publications (ISSN 1437-4447)},
Title = {Lectures on {Jacques Herbrand} as a Logician},
OPTurl = {http://arxiv.org/abs/0902.4682},
doi = {10.48550/ARXIV.0902.4682},
Year = 2009,
}
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