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 Besides the well-known correction of Herbrand's False Lemma by Goedel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its consequences on Herbrand's Modus Ponens Elimination.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 Besides the well-known correction of Herbrand's False Lemma by Goedel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its consequences on Herbrand's Modus Ponens Elimination.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}, Addendum = {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, }