Lectures on Jacques Herbrand as a Logician (bibtex)
by Claus-Peter Wirth, Jörg Siekmann, Christoph Benzmüller, Serge Autexier
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 Besides the well-known correction of Herbrand's False Lemma by Goedel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its consequences on Herbrand's Modus Ponens Elimination.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.
Reference:
Lectures on Jacques Herbrand as a Logician (Claus-Peter Wirth, Jörg Siekmann, Christoph Benzmüller, Serge Autexier), SEKI Publications (ISSN 1437-4447), 2009. (arXiv:0902.4682)
Bibtex Entry:
@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                  Dreben, we also present the hardly known unpublished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},
  Url =		 {http://arxiv.org/abs/0902.4682},
  Year =	 2009,
}
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