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Gentzen Gerhard:     more detail

The collected papers of Gerhard Gentzen (Studies in logic and the foundations of mathematics) by Gerhard Gentzen, 1969 Gerhard Gentzen German Logicians: Immanuel Kant, Gottfried Leibniz, Georg Cantor, Gottlob Frege, Gerhard Gentzen, Christoph Gottfried Bardili People From the Province of Pomerania: Edward Sapir, Rudolf Virchow, Gerhard Gentzen, Carl Meinhof, Hermann Grassmann, Max Schmeling Academics of the Charles University: Albert Einstein, Jan Hus, Ernst Mach, Ewald Hering, Gerhard Gentzen, Tomás Garrigue Masaryk, Alfred Weber People From Greifswald: Caspar David Friedrich, Gerhard Gentzen, Robin Szolkowy, Hans Fallada, Magnus Von Braun, Toni Kroos, Kurt Wolff Recherches Sur La Deduction Logique by Gerhard GENTZEN, 1955 Kolmogorov, Heyting and Gentzen on the intuitionistic logical constants *.: An article from: Crítica by Gustavo Fernandez Diez, 2000-12-01 Die Gegenwartige Lage in der Mathematischen Grundlagenforschung [bound with] Neue Fassung des Widerspruchsfreiheitsbeweises fur die Reine Zahlentheorie. [Facsimile reprint of 1938- text in Fraktur] by Gerhard Gentzen, 1969-01-01 Patrones inferenciales.: An article from: Crîtica by Axel Arturo Barcelô Aspeitia, 2008-12-01 Logic's Lost Genius (History of Mathematics) by Eckart Menzler-Trott, 2007-11-21 Natural Deduction: A Proof-Theoretical Study by Dag Prawitz, 2006-02-24

lists with details

41. Interrogation AUTEUR:279
    Translate this page AUTEUR gentzen, gerhard. 1 réponse. Recherches sur la deduction logique -gentzen, gerhard - PUF - 1955.  
    http://www.loria.fr/cgi-bin/DorisWeb/bibrebond?AUTEUR:279

42. Austrian Literature Online - Kataloge
    gentzen, gerhard gentzen, gerhard gentzen, gerhard - 1969  
    http://webapp.uibk.ac.at/alo/cat/?id=5007167

43. Gerhard Schroder Spd Minister Chancellor Schroder's Succeeds
    gerhard Fritz Kurt Schroder gehat rod (born April 7, 1944), a German politician,has be, gerhard gentzengerhard gentzen ( November 24, 1909 August 4,  
    http://www.economicexpert.com/a/Gerhard:Schroder.htm
    
    Extractions: var GLB_RIS='http://www.economicexpert.com';var GLB_RIR='/cincshared/external';var GLB_MMS='http://www.economicexpert.com';var GLB_MIR='/site/image';GLB_MML='/'; document.write(''); document.write(''); document.write(''); document.write(''); A1('s',':','html'); Non User A B C ... First Prev [ 1 Next Last (7th of the Federal Republic) Term of Office: October 27 Predecessor: Helmut Kohl Date of Birth: April 7 Political Party SPD Profession ... lawyer Gerhard Fritz Kurt Schröder April 7 ), a German politician , has been serving since 1998 as Chancellor of Germany . His political career has unfolded within the left-of-center Social Democratic Party of Germany Sozialdemokratische Partei Deutschlands SPD ) - for a time he also served as Party Chairman. He heads a coalition of the SPD and the German Green Party . Before becoming a fulltime politician, he was a lawyer. (His surname often appears spelled Schroeder in English The English language is a West Germanic language, originating from England. It is the third most common "first" language (native speakers), with around 402 million people in 2002. English has lingua franca status in many parts of the world, due to the mil

44. Gerhard Gentzen Biography .ms
    ME Szabo. Collected Papers of gerhard gentzen. NorthHolland, 1969. degerhardgentzen esgerhard gentzen plgerhard gentzen  
    http://gerhard-gentzen.biography.ms/
    
    Extractions: Gerhard Gentzen November 24 August 4 ) was a German mathematician and logician Born in Greifswald Germany , he died in Prague Czechoslovakia in a prisoner of war camp, after being arrested by the Russians due to his Nazi loyalties. He was one of Weyl 's students at the University of Göttingen from to . His main work was on the foundations of mathematics , in proof theory , specifically natural deduction and the sequent calculus . His cut-elimination theorem is the cornerstone of proof-theoretic semantics , and some philosophical remarks in his "Investigations into Logical Deduction", together with Wittgenstein's aphorism that "meaning is use", constitute the starting point for inferential role semantics Related Links Gerhard Schroeder quotes Gerhard Kocher quotes Gerhard Gschwandtner quotes Eckart Menzler-Trott. Gentzens Problem: Mathematische Logik im nationalsozialistischen Deutschland. Birkhäuser Verlag, 2001. ISBN 3-7643-6574-9. An English translation is planned. M. E. Szabo. Collected Papers of Gerhard Gentzen. North-Holland, 1969.

45. The Mathematics Genealogy Project - Gerhard Gentzen
    Translate this page gerhard gentzen Biography. Dr. phil. Georg-August-Universität Göttingen 1934.Germany. Dissertation Untersuchungen über das logische Schließen  
    http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=52969

46. The Mathematics Genealogy Project - Update Data For Gerhard Gentzen
    If you have Mathematics Subject Classifications to submit for an entire group ofindividuals (for instance all those that worked under a particular advisor)  
    http://www.genealogy.math.ndsu.nodak.edu/html/php/submit-update.php?id=52969

47. Lexikon Gerhard Gentzen
    gerhard gentzen aus der freien Enzyklopädie  
    http://lexikon.freenet.de/Gerhard_Gentzen
    
    Extractions: Sie sind hier: Startseite Lexikon Gerhard Gentzen Gerhard Karl Erich Gentzen 24. November in Greifswald 4. August in Prag ) war ein deutscher Mathematiker und Logiker Gentzen ist ein wichtiger Mitbegr¼nder der modernen mathematischen Beweistheorie . Die nachhaltige Bedeutung der von ihm entwickelten Methoden, Regeln und Strukturen zeigt sich heute vor allem in wichtigen Teilgebieten der Informatik, der Verifikation von Programmen. Dabei werden formale Beweise selbst als Programme gedeutet. Ausgehend von dem Hilbertschen Programm bewies Gentzen f¼r den Aufbau der Mathematik die Widerspruchsfreiheit der Zahlentheorie . Er entwickelte als einer der ersten Systeme nat¼rlichen SchlieŸens , f¼r die er auch den sogenannten " Hauptsatz " bewies. Dadurch sind groŸe Teile der Logik und Mathematik als widerspruchsfrei beweisbar.

48. List Of Scientists By Field
    Translate this page gentzen, gerhard. gentzen, gerhard. Geoffroy Saint-Hilaire, Étienne. GeoffroySaint-Hilaire, Isidore. Geoffroy, Claude Joseph. Geoffroy, Claude Joseph  
    http://www.indiana.edu/~newdsb/g.html
    
    Extractions: Gabb, William More Gabor, Dennis Gabor, Dennis Gabriel, Siegmund Gadolin, Johan Gadolin, Johan Gaede, Wolfgang Gaertner, Joseph Gaertner, Karl Friedrich von Gaffky, Georg Theodor August Gaffky, Georg Theodor August Gagliardi, Domenico Gagliardi, Domenico Gahn, Johan Gottlieb Gahn, Johan Gottlieb Gaillot, Aimable Jean-Baptiste Gaillot, Aimable Jean-Baptiste Gaimard, Joseph Paul Gaimard, Joseph Paul Gaimard, Joseph Paul Gaines, Walter Lee Galeazzi, Domenico Gusmano Galeazzi, Domenico Gusmano Galeazzi, Domenico Gusmano Galen Galerkin, Boris Grigorievich Galerkin, Boris Grigorievich Galilei, Galileo Galilei, Galileo Galilei, Vincenzio Gall, Franz Joseph Gall, Franz Joseph Galle, Johann Gottfried Gallois, Jean Galois, Evariste Galton, Francis Galton, Francis Galton, Francis Galvani, Luigi Galvani, Luigi Galvani, Luigi Gamaleya, Nikolay Fyodorovich Gambey, Henri-Prudence Gamow, George Garbasso, Antonio Giorgio Garnett, Thomas Garnett, Thomas Garnot, Prosper Garnot, Prosper Garnot, Prosper Garnot, Prosper Garreau, Lazare Garrod, Archibald Edward Garrod, Archibald Edward

49. Philosophy And Religion
    gentzen, gerhard. Giles of Lessines. Glanvill, Joseph. Glisson, Francis.Gravesande, Willem Jacob s. Green, George. Greenwood, Isaac  
    http://www.indiana.edu/~newdsb/phil.html
    
    Extractions: Philosophy and Religion Abailard, Pierre Abano, Pietro d' Adanson, Michel Agol, Izrail' Iosifovich Agrippa, Heinrich Cornelius von Ailly, Pierre d' Alain de Lille, Alanus de Albert of Saxony Alcmaeon of Crotona Alexander of Aphrodisias Alsted, Johann Heinrich Ames, William Ammonius, Son of Hermias Anatolius of Alexandria Anaxagoras Anaximander Anaximenes of Miletus Andreae, Johann Valentin Apelt, Ernst Friedrich Aquinas, Saint Thomas Archytas of Tarentum Argoli, Andrea Augustine of Hippo, Saint, Aurelius Bachelard, Gaston Bacon, Francis Bacon, Roger Bain, Alexander Baranzano, Giovanni Antonio Bartholin, Caspar Basso, Sebastian Bede, the Venerable Bellarmine, Robert Bergson, Henri-Louis Berkeley, George Bernard of Chartres, Bernardus Bernard of Le Treille Bernard Silvestre, Bernard de Bickerton, Alexander William Bisterfeld, Johann Heinrich Blasius of Parma Boehme, Jacob Boethius, Anicius Manlius Severinus Bogdanov, Aleksandr Aleksandrovich Bohr, Niels Henrik David Bolzano, Bernard Bonnet, Charles Borro, Girolamo Boullanger, Nicolas-Antoine Bourguet, Louis

50. Semantic Networks
    gerhard gentzen (1935) showed that a collection of implications in that form could gentzen, gerhard (1935) Untersuchungen über das logische Schließen,  
    http://www.jfsowa.com/pubs/semnet.htm
    
    Extractions: John F. Sowa A semantic network or net is a graphic notation for representing knowledge in patterns of interconnected nodes and arcs. Computer implementations of semantic networks were first developed for artificial intelligence and machine translation, but earlier versions have long been used in philosophy, psychology, and linguistics. What is common to all semantic networks is a declarative graphic representation that can be used either to represent knowledge or to support automated systems for reasoning about knowledge. Some versions are highly informal, but other versions are formally defined systems of logic. Following are six of the most common kinds of semantic networks, each of which is discussed in detail in one section of this article. Definitional networks emphasize the subtype or is-a relation between a concept type and a newly defined subtype. The resulting network, also called a generalization or subsumption hierarchy, supports the rule of inheritance for copying properties defined for a supertype to all of its subtypes. Since definitions are true by definition, the information in these networks is often assumed to be necessarily true.

51. Analogical Reasoning
    gentzen, gerhard (1935) Untersuchungen über das logische Schließen, translatedas Investigations into logical deduction in The Collected Papers of  
    http://www.jfsowa.com/pubs/analog.htm
    
    Extractions: John F. Sowa and Arun K. Majumdar VivoMind LLC Abstract canonical formation rules for conceptual graphs, are widely used in CG systems for language understanding and scene recognition as well as analogy finding and theorem proving. The same algorithms used to optimize analogy finding can be used to speed up all the methods of reasoning based on the canonical formation rules. Conceptual Structures for Knowledge Creation and Communication , LNAI 2746, Springer-Verlag, pp. 16-36. Note: Before discussing the use of analogy in reasoning, it is important to analyze the concept of analogy and its relationship to other cognitive processes. General-purpose dictionaries are usually a good starting point for conceptual analysis, but they seldom go into sufficient depth to resolve subtle distinctions. A typical dictionary lists synonyms for the word analogy , such as similarity resemblance , and correspondence . Then it adds more specialized word senses, such as a similarity in some respects of things that are otherwise dissimilar a comparison that determines the degree of similarity , or an inference based on resemblance or correspondence . In AI, analogy-finding programs have been written since the 1960s, but they often use definitions of analogy that are specialized to a particular application.

52. Sequent Calculus -- From MathWorld
    The classical (multisuccedent) variant due to gentzen is called LK, REFERENCES.gentzen, G. The Collected Papers of gerhard gentzen (Ed. ME Szabo).  
    http://mathworld.wolfram.com/SequentCalculus.html
    
    Extractions: MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Logic General Logic ... Sakharov Sequent Calculus A sequent is an expression , where and are (possibly empty) sequences of formulas. Here, is called the antecedent and is called the consequent. The informal understanding of sequents is that the sequent corresponds to . The initial sequent of all derivations is The rules of inference for sequent calculus are divided in two categories: structural and logical. There are at least two logical rules for every propositional connective and every quantifier; one of them applies to the antecedent, whereas the other applies to the consequent. The structural rules are thinning, contraction, exchange, and cut, The logical rules are given by conjunction, disjunction, negation, implication, universal quantifier

53. Cut Elimination Theorem -- From MathWorld
    REFERENCES. gentzen, G. The Collected Papers of gerhard gentzen (Ed. ME Szabo).Amsterdam, Netherlands NorthHolland, 1969.  
    http://mathworld.wolfram.com/CutEliminationTheorem.html
    
    Extractions: MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Logic General Logic ... Sakharov Cut Elimination Theorem The cut elimination theorem, also called the "Hauptsatz" (Gentzen 1969), states that every sequent calculus derivation can be transformed into another derivation with the same endsequent (bottom sequent) and in which the cut rule does not occur. All derivations without cuts posses the sub-formula property that all formulas occurring in a derivation are sub-formulas of the formulas from the endsequent. A sharpened form of theorem applies to the classical variant of sequent calculus. This form states that any derivation can be transformed to another derivation with the same endsequent and having the following properties. 1. It has no cuts. 2. It contains a so-called midsequent whose derivation contains no and , and the only inference rules occurring in the derivation below the midsequent are the and rules and structural rules.

54. Gerhard Gentzen
    http://www.netzwelt.de/lexikon/Gerhard_Gentzen.html

55. Proof Theory - Wikipedia, The Free Encyclopedia
    In parallel with the proof theoretic work of Gödel, gerhard gentzen was layingthe foundations In ME Szabo, editor, Collected Papers of gerhard gentzen.  
    http://en.wikipedia.org/wiki/Proof_theory
    
    Extractions: Over US$155,000 has been donated since the drive began on 19 August. Thank you for your generosity! Proof theory , studied as a branch of mathematical logic , represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures , such as plain lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. As such, proof theory is closer to syntax , while model theory is more purely semantical . Together with model theory axiomatic set theory , and recursion theory , proof theory is one of the so-called four pillars of the foundations of mathematics That represents the position as of about onwards. The subject of proof theory has a significant if somewhat opaque prehistory as metamathematics , the proposed theory under development since the start of the twentieth century , which was, for a generation, under the influence of David Hilbert . The aim of a convincing consistency proof for mathematics was not to be realised, for reasons only later understood: proof theory can only sweep the metaphysical dust into tidier heaps under carpets with more attractive patterns. Hilbert's ideas seem to have been based on an analogy, in fact false, with the

56. Collected Works In Mathematics And Statistics
    gerhard gentzen, Sophie Germain, J. Willard Gibbs, Kurt Gödel gentzen, gerhard,19091945, The collected papers of gerhard gentzen, 1, QA 9 G329, Killam  
    http://www.mathstat.dal.ca/~dilcher/collwks.html
    
    Extractions: This is a list of Mathematics and Statistics collected works that can be found at Dalhousie University and at other Halifax universities. The vast majority of these works are located in the Killam Library on the Dalhousie campus. A guide to other locations is given at the end of this list. If a title is owned by both Dalhousie and another university, only the Dalhousie site is listed. For all locations, and for full bibliographic details, see the NOVANET library catalogue This list was compiled, and the collection is being enlarged, with the invaluable help of the Bibliography of Collected Works maintained by the Cornell University Mathematics Library. The thumbnail sketches of mathematicians were taken from the MacTutor History of Mathematics Archive at the University of St. Andrews. For correction, comments, or questions, write to Karl Dilcher ( dilcher@mscs.dal.ca You can scroll through this list, or jump to the beginning of the letter: [On to B] [Back to Top]

57. Gerhard Johann David Von Scharnhorst - Encyclopedia Article About Gerhard Johann
    Information about gerhard Johann David von Scharnhorst in Free online Englishdictionary and gerhard gentzen gerhard Glogowski gerhard Herzberg  
    http://encyclopedia.thefreedictionary.com/Gerhard Johann David von Scharnhorst

58. Proof Technology
    seminal work of gerhard gentzen on Natural Deduction (ND) and Sequent Calculi.gentzen introduced the Ncalculi (NK, NJ for classical and Intuitionistic  
    http://www.cs.cornell.edu/Info/Projects/NuPrl/Intro/ProofTech/technology.html
    
    Extractions: Nuprl is a proof development system. Much of our effort has gone into a technology for creating and displaying proofs. When we talk about proofs in our writing, we generally mean formal proofs. This is especially true under this heading of proof technology. While the idea of a proof in the sense discovered by the Greeks and used centrally in mathematics since then is widely used, the technical notion of proof that we have in mind is relatively new, since the 1970s, and much of our technical work has contributed to creating a new notion of formal proof, one that incorporates computer programs (called tactics) to fill in details, and one that allows computers to carry out various kinds of steps such as calculation, symbolic evaluation and rewriting of one term to another. The central new idea that we introduced is called a tactic-tree proof. It built on and extended the idea pioneered in the Edinburgh LCF system of a tactic. The underlying basis of tactic-tree proofs is the notion of a sequent. Gentzen introduced sequent based proof systems, his L-systems . But we wanted to present proofs in a top-down refinement style rather than Gentzen's bottom-up style. This led us to presentations of sequent proofs in the style of Beth's tableaux . Following Bates , we call this top down sequent logic a Refinement Logic (RL) Our first writing on Refinement Logics is Joe Bate's thesis . This is also the primitive logic of the article Proofs as Programs . The idea is that proofs are interactively built by refining a single goal into subgoals using an inference rule.

59. Arché TWiki . Main . SzaboCollectedPapersOfGerhardGentzen
    Book M Szabo, The collected papers of gerhard gentzen, (Amsterdam, NorthHolland1969). This citation belongs to the following research topics  
    http://weka.ucdavis.edu/~ahwiki/bin/view/Main/SzaboCollectedPapersOfGerhardGentz
    
    Extractions: Main Arché Dept TWiki ... Sandbox Changes Search M Szabo, The collected papers of Gerhard Gentzen (Amsterdam, North-Holland: 1969) This citation belongs to the following research topics: MathBibConvert 17 Feb 2003 Warning: This bibliography entry has an unknown publisher. See BibliographyCheck for details. BookCitation Year: Publisher: Amsterdam, North-Holland Title: The collected papers of Gerhard Gentzen Author: M Szabo Topic SzaboCollectedPapersOfGerhardGentzen Edit Attach Ref-By Print Diffs More Revision r1.1 - 09 Mar 2004 - 17:48 - MarcusRossberg

60. Materialien Zur Kontroverse Um "das" Unendliche
    Translate this page gentzen, gerhard (1936). Der Unendlichkeitsbegriff in der Mathematik. gentzen,gerhard (1937). Unendlichkeitsbegriff und Widerspruchsfreiheit der  
    http://www.sgipt.org/wisms/geswis/mathe/m_unend0.htm
    
    Extractions: Anfang Kontroverse Unendlich Rel. Aktuelles Titelblatt Konzept Archiv ... Wichtige Hinweise zu externen Links und Empfehlungen Willkommen in der Abteilung Wissenschaft in unserer Internet-Publikation GIPT Bereich Geschichte der Wissenschaften, hier Mathematik speziell zum Thema: Materialien zur Kontroverse um "das" Unendliche von Rudolf Sponsel, Erlangen

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