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         Gentzen Gerhard:     more detail
  1. The collected papers of Gerhard Gentzen (Studies in logic and the foundations of mathematics) by Gerhard Gentzen, 1969
  2. Gerhard Gentzen
  3. German Logicians: Immanuel Kant, Gottfried Leibniz, Georg Cantor, Gottlob Frege, Gerhard Gentzen, Christoph Gottfried Bardili
  4. People From the Province of Pomerania: Edward Sapir, Rudolf Virchow, Gerhard Gentzen, Carl Meinhof, Hermann Grassmann, Max Schmeling
  5. Academics of the Charles University: Albert Einstein, Jan Hus, Ernst Mach, Ewald Hering, Gerhard Gentzen, Tomás Garrigue Masaryk, Alfred Weber
  6. People From Greifswald: Caspar David Friedrich, Gerhard Gentzen, Robin Szolkowy, Hans Fallada, Magnus Von Braun, Toni Kroos, Kurt Wolff
  7. Recherches Sur La Deduction Logique by Gerhard GENTZEN, 1955
  8. Kolmogorov, Heyting and Gentzen on the intuitionistic logical constants *.: An article from: Crítica by Gustavo Fernandez Diez, 2000-12-01
  9. 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
  10. Patrones inferenciales.: An article from: Crîtica by Axel Arturo Barcelô Aspeitia, 2008-12-01
  11. Logic's Lost Genius (History of Mathematics) by Eckart Menzler-Trott, 2007-11-21
  12. Natural Deduction: A Proof-Theoretical Study by Dag Prawitz, 2006-02-24

21. Citations: Studies In Logic And The Foundations Of Mathematics - Szabo, Collecte
M. E. Szabo, editor. The Collected Papers of gerhard gentzen. Studies in Logic and the Foundations of Mathematics. NorthHolland, 1969.
http://citeseer.nj.nec.com/context/292692/0
14 citations found. Retrieving documents...
M.E. Szabo. Algebra of Proofs. Studies in Logic and the Foundations of Mathematics , 88(1978), North-Holland P.C.
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This paper is cited in the following contexts: Proof of a Conjecture of S. Mac Lane - Soloviev (1996) (Correct) ....or rational numbers) are commutative since about 1963. Although in this way the problem became more or less generally known, I am unaware of a published record. M . Barr (e mail to the author) suggested a similar question (not published) independently about 1970. In Algebra of Proofs by M. E Szabo , chapter 8, one can find an assertion that a diagram is commutative in a free SMC category iff every its interpretation in the SMC category of real Banach spaces is commutative. The following statement can be found in [1] 1979) Theorem A diagram commutes in all closed symmetric monoidal ....
....categories iff it commutes in the category of real vector spaces. It is formulated in the appendix (by Po Hsuang Chu, introducing the Chu construction ) with the reference to a paper Commutativity in Closed Categories by Szabo, apparently never published. However, soon after the appearance of

22. Citations: Investigations Into Logical Deduction - Gentzen (ResearchIndex)
gentzen, G. Investigations into logical deduction. In The Collected Papers of gerhard gentzen, M. E. Szabo, Ed. NorthHolland, 1969, pp. 68131. Retrieving documents G. gentzen. Investigations into logical deductions
http://citeseer.nj.nec.com/contextsummary/312/0
113 citations found. Retrieving documents...
Gerhard Gentzen. Investigations into logical deductions , 1935. In M. E. Szabo, editor, The Collected Papers of Gerhard Gentzen, pages 68-131. North-Holland Publishing Co., Amsterdam, 1969.
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This paper is cited by the following papers:
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A modular, tactic-based approach to first-order temporal.. - Castellini, Smaill (2000)
(Correct)
Non-deterministic Semantics for Intuitionistic.. - School Of Computer
... (4 citations) Self-citation (Gentzen) (Correct)
Classical Gentzen-type Methods in Propositional Many-Valued Logics - Avron
Self-citation (Gentzen) (Correct)
Canonical Propositional Gentzen-Type Systems - Avron, Lev
Self-citation (Gentzen) (Correct)
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23. Encyclopedia: Gerhard Gentzen
Factoid 55. Japan has 53 working nuclear reactors and is planningto build another 12. Interesting Facts. Make your own graph Hold
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    Encyclopedia : Gerhard Gentzen
    Gerhard Gentzen November 24 August 4 ) was a German mathematician and logician.

    24. Semantic Networks
    gentzen, gerhard (1935) "Untersuchungen über das logische Schließen " translated as "Investigations into in The Collected Papers of gerhard gentzen, ed. and translated by M
    http://www.jfsowa.com/pubs/semnet.htm
    Semantic Networks
    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.
  • 25. The Mathematics Genealogy Project - Gerhard Gentzen
    Select a mirror NDSU (main) AMS Bielefeld Ole Miss IMPA. gerhard GentzenBiography Dr. phil. GeorgAugust-Universität Göttingen 1934.
    http://www.genealogy.ams.org/html/id.phtml?id=52969

    26. Analogical Reasoning
    Analogical Reasoning. John F. Sowa and Arun K. Majumdar. VivoMind LLC. Abstract. gentzen, gerhard (1935) "Untersuchungen über das logische Schließen " translated as "Investigations into in The Collected Papers of gerhard gentzen, ed. and translated by M
    http://www.jfsowa.com/pubs/analog.htm
    Analogical Reasoning
    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:
    1. Analogy and Perception
    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.

    27. LING 426 Mathematical Linguistics Autumn 2001 Time And Place By
    Higherorder Modal Logic. North- Holland.gentzen, gerhard. 1934. Untersuchungen ¨uber das logische The Collected Papers of gerhard gentzen. Amsterdam North-Holland.Wilcox, Rand R
    http://www.people.cs.uchicago.edu/~sfulop/Ling426syll.pdf

    28. Gerhard Gentzen :: Online Encyclopedia :: Information Genius
    gerhard gentzen. Online Encyclopedia gerhard gentzen (November 24,1909 August 4, 1945) was a German mathematician and logician.
    http://www.informationgenius.com/encyclopedia/g/ge/gerhard_gentzen.html
    Quantum Physics Pampered Chef Paintball Guns Cell Phone Reviews ... Science Articles Gerhard Gentzen
    Online Encyclopedia

    Gerhard Gentzen November 24 August 4 ) was a German mathematician and logician Born in Greifswald Germany , he died in Prague Czechoslovakia 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 This content from wikipedia is licensed under the GNU Free Documentation License Power Supplies Hardware Information Law Advice

    29. Auteur - Gentzen, Gerhard
    gentzen,gerhard AMSTERDAM.LONDON NORTH-HOLLAND PUBLISHING COMPANY , 1969, XI-338.
    http://www.math.univ-rennes1.fr/bibli/catalogue/Auteur.htm?numrec=06195494691367

    30. Fiche Document -COLLECTED PAPERS OF GERHARD GENTZEN (THE)
    gentzen, gerhard AMSTERDAM.LONDON NORTH-HOLLAND
    http://www.math.univ-rennes1.fr/bibli/catalogue/Document.htm&numrec=031900480918
    Accueil Index Auteur
    Type de document
    Thesaurus
    Recherche
    Simple
    Expert
    Affiner la recherche
    Revues
    Mes paniers Mon panier Nouveau panier Affiner la recherche (1 Documents) Chercher ? Mots du titre
    Auteurs
    Source
    Commentaire Autres champs aaaa aaaa, mm/aaaa, jj/mm/aaaa Titre exact CD Colloque Livre Revue VIDEO Livre - Cote : 03/SZA - (disponible) Ajouter Imprimer Envoyer par mail AMSTERDAM.LONDON Collection : STUDIES IN LOGIC AND THE FOUNDATIONS OF MATHEMATICS Type doc RNBM : O Langue : A Exemplaires
      1 - 03F/SZA
    Fax 02 23 23 67 90 email bibirmar@univ-rennes1.fr Mon espace Mes paniers Recherche rapide Identification Identifiant : Mot de passe :

    31. Janus: The Papers Of Alan Mathison Turing
    42, Offprints of three articles by gerhard gentzen. 43, The Physical Principlesof the Quantum Theory . Creator, gentzen, gerhard. Covering Dates, 19361937.
    http://janus.lib.cam.ac.uk/db/node.xsp?id=EAD/GBR/0272/AMT/B/42

    32. Janus: The Papers Of Alan Mathison Turing
    1953. AMT/B/42, Offprints of three articles by gerhard gentzen. The file comprises. 1937.Origination gentzen, gerhard. 3 items in envelope; paper. 19361937.
    http://janus.lib.cam.ac.uk/db/node.xsp?id=EAD/GBR/0272/AMT/B;recurse=1

    33. Seznam Osob Podle Jména: Ge
    Artemesia, malír; Jemný, Marie, Britové spisovatel scifi; Gento,atlet; gentzen, gerhard, (1909-1945), matematik; Geoffrey Monmouthu
    http://wikipedia.infostar.cz/l/li/list_of_people_by_name__ge.html
    švodn­ str¡nka Tato str¡nka v origin¡le
    Seznam osob podle jm©na: Ge
    Seznam osob podle jm©na B C D ... F G H J K ... Ga-Gd Ge Gf-Gh Gi Gj-Gl Gm-Gn ... J­t - Gp - Gq - Gr Gs - Gt - Gu Gv Gw - Gx - Gy Gz

    34. Browse The Turing Digital Archive
    Browse the Turing Digital Archive. Contents of AMT/B/42 (up to B/3357).gentzen, gerhard. Off-print, ‘Die Widerspruchfreiheit der
    http://www.turingarchive.org/browse.php/B/42
    Browse the Turing Digital Archive
    Contents of AMT/B/42 ( up to B/33-57
    Gentzen, Gerhard Off-print, ‘Die Widerspruchfreiheit der reinen Zahlentheorie’ from Mathematische Annalen , (Vol. 112, No. 4, 1936); Off-print, ‘Die Widerspruchfreiheit der Stufenlogik’ from Mathematische Zeitschrift , (Vol. 41, No. 3, 1936); Off-print, ‘Unendlichkeitsbegriff und Widerspruchfreiheit der Mathematik’ from Actualités Scientifiques et Industrielles , the Report of IXth International Congress of Philosophy, Paris 1-6 Aug. 1937. Paper, 3 items in envelope. Printed Keywords: ‘Die Widerspruchfreiheit der reinen Zahlentheorie’; ‘Die Widerspruchfreiheit der Stufenlogik’; Gentzen, Gerhard; ‘Unendlichkeitsbegiff und Widerspruchfreiheit der Mathematik’ Provenance: Presented to the Archive Centre in May 1996 by Professor Michael Yates, Robin Gandy's executor. The material was previously in the possession of Robin Gandy who had been one of AMT's executors. No scans available for this item.

    35. Index Of The Turing Digital Archive
    General tensors in a group’, C/13; gentzen, gerhard,B/42; Gepp,, A/19; Gervis, Ruth, A/19; Gill, Stanley, B/38;
    http://www.turingarchive.org/index/
    Index of the Turing Digital Archive
    If you can't find what you want in this index, try searching for some key words or phrases or try browsing by category.
    • ‘A diffusion reaction theory of morphogenesis in plants’, C/7
    • ‘A formal theorem in Church’s theory of types’, B/29
    • ‘A method for the calculation of the zeta-function’, B/17
    • ‘A new mechanism which slows simple conditioning’, B/34
    • ‘A note on normal numbers.’, C/15
    • ‘A practical form of type theory I’, B/3
    • ‘A practical form of type theory II’, C/6
    • A.M. Turing Award, A/24
    • A.M. Turing’s Original Proposal for the Development of an Electronic Computer, B/25
    • Abraham, M., B/33
    • ACE (Automatic Computing Engine), B/1 B/2 C/32
    • Alan Turing : the Enigma, A/38 A/40 D/11 D/12 ... D/13
    • Alexander, C. Hugh, A/17
    • Almost periodic functions, B/10 D/11
    • ‘An electrical hypothesis of central inhibition ...’, B/48
    • Andrews, A.J.P., A/15
    • ‘Another proof’, C/23
    • Ashby, W. Ross, B/34
    • Association of Computing Machinery, A/24
    • Bachman, Charles W., A/24
    • Ball, W.W. Rouse, B/35
    • Bates, John A.V., A/5
    • Baum, Rudy M., A/40
    • Bayley, Don, A/5
    • BBC, B/5 B/6
    • ‘Bemerkungen zu den Grundlagen der Geometrie’

    36. Gerhard Gentzen Definition Meaning Information Explanation
    WoLLIC 2000 gentzen33 gentzen, gerhard, Über das 193217, 1989. Szabo69 Szabo, ME,The Collected Papers of gerhard gentzen, North-Holland, Amsterdam, 1969.
    http://www.free-definition.com/Gerhard-Gentzen.html
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    Gerhard Gentzen
    Gerhard Gentzen November 24 August 4 ) was a German mathematician and logician Born in Greifswald Germany , he died in Prague Czechoslovakia He was one of Weyl 's students at the University of G¶ttingen from to . His main work was on the foundations of mathematics , in proof theory Books about 'Gerhard Gentzen' at: amazon.com or amazon.co.uk Note: This article from Wikipedia is made available under the terms of the GNU FDL
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    37. Logikùv Rok
    Translate this page Herbrand, Jean, (+ 1931). Srpen. 4. 8. Venn, John, (* 1834). gentzen, gerhard, (+1945). 6. 8. Arnauld, Antoine, (+ 1694). 11. gentzen, gerhard, (* 1909). Prosinec.2. 12.
    http://www.volny.cz/logici/vyroci/
    Logikùv rok
    Leden Únor Bøezen Duben ... Prosinec
    Leden
    Kleene, Stephen Cole Cantor, Georg Hintikka, Jaakko Carroll, Lewis Tarski, Alfred Gödel, Kurt Ramsey, Frank Plumpton Hilbert, David Kleene, Stephen Cole Carroll, Lewis
    Únor
    Russell, Bertrand Artur William Lewis, Clarence Irving Arnauld, Antoine von Neumann, Johannes Post, Emil Leon Herbrand, Jean Dedekind, Richard £ukasiewicz, Jan Hilbert, David Whitehead, Alfred North Nicod, Jean Fraenkel, Adolf Abraham Ramsey, Frank Plumpton Brouwer, Luitzgen Egbertus Jan
    Bøezen
    Cantor, Georg Barwise, Jon Davidson, Donald Montague, Richard de Morgan, Augustus Carnap Rudolf Skolem, Thoralf Lorenzen, Paul Ackermann, Wilhelm
    Duben
    Vaught, Robert Lawson Venn, John Vaught, Robert Lawson Lewis, Clarence Irving Peirce, Charles Sanders Peano, Giuseppe Post, Emil Leon Wittgenstein, Ludwig Gödel, Kurt Wittgenstein, Ludwig
    Kvìten
    Löwenheim, Leopold Heyting, Arend Wang, Hao Russell, Bertrand Arthur William Wang, Hao Zermelo, Ernst Skolem, Thoralf
    Èerven
    Turing, Alan Mathison Church, Alonzo von Wright, Georg Henrik von Wright, Georg Henrik Turing, Alan Mathison

    38. Logician's Year
    August. 4 Aug, Venn, John, (* 1834). gentzen, gerhard, (+ 1945). 14 Nov, Leibniz,Gottfried Wilhelm von, (+ 1716). 24 Nov, gentzen, gerhard, (* 1909). December.
    http://www.volny.cz/logici/vyroci/english.html
    The Logician's Year
    January February March April ... December
    January
    5 Jan Kleene, Stephen Cole 6 Jan Cantor, Georg 12 Jan Hintikka, Jaakko 14 Jan Carroll, Lewis Tarski, Alfred Gödel, Kurt 19 Jan Ramsey, Frank Plumpton 23 Jan Hilbert, David 26 Jan Kleene, Stephen Cole 27 Jan Carroll, Lewis
    February
    2 Feb Russell, Bertrand Artur William 3 Feb Lewis, Clarence Irving 6 Feb Arnauld, Antoine 8 Feb von Neumann, Johannes 11 Feb Post, Emil Leon 12 Feb Herbrand, Jean Dedekind, Richard 13 Feb £ukasiewicz, Jan 14 Feb Hilbert, David 15 Feb Whitehead, Alfred North 16 Feb Nicod, Jean 17 Feb Fraenkel, Adolf Abraham 22 Feb Ramsey, Frank Plumpton 27 Feb Brouwer, Luitzgen Egbertus Jan
    March
    3 Mar Cantor, Georg 5 Mar Barwise, Jon 6 Mar Davidson, Donald 7 Mar Montague, Richard 18 Mar de Morgan, Augustus Carnap Rudolf 23 Mar Skolem, Thoralf 24 Mar Lorenzen, Paul 25 Mar Ackermann, Wilhelm
    April
    2 Apr Vaught, Robert Lawson 4 Apr Venn, John Vaught, Robert Lawson 12 Apr Lewis, Clarence Irving 19 Apr Peirce, Charles Sanders 20 Apr Peano, Giuseppe 21 Apr Post, Emil Leon 26 Apr Wittgenstein, Ludwig 28 Apr Gödel, Kurt

    39. Index
    Translate this page I Aussagenlogik Semantischer Schlussbegriff I Aussagenlogik Semantischer SchlussbegriffII Prädikatenlogik gentzen, gerhard Syntax gentzen-Kalkül see
    http://logik.phl.univie.ac.at/~chris/skriptum/node78.html

    Prädikatenlogik der ersten Stufe
    Vorherige Seite: Sonstige zitierte Literatur Inhalt
    Index
    ukasiewicz-Notation
    see polnische Notation
    ukasiewicz, Jan
    Exkurs: Polnische Notation
    see Konjunktion
    see Disjunktion
    see Konditional
    see Negation
    Syntaktischer Schlussbegriff
    Semantischer Schlussbegriff I: Aussagenlogik
    see Bikonditional
    see Lekton
    Abendstern
    Freges Bedeutungstheorie
    Abhängigkeit
    des Ergebnisses der Anwendung einer Transformationsregel
    see die betroffene Regel
    Abkürzungen
    Verwendete Zeichen und Abkürzungen to Einige griechische Buchstaben
    Ableitung
    Syntaktischer Schlussbegriff
    Ableitungsregel
    see Transformationsregel
    actual world (engl.)
    see tatsächliche Welt
    Addition
    unvollständige
    see Vernam-Chiffrierschritt
    Alle
    see Quantor
    Allquantor
    Bausteine Formationsregeln
    beseitigen
    Regel der Allquantor-Beseitigung (
    einführen
    Regel der Allquantor-Einführung (
    Allquantor-Beseitigung
    see Regel der Allquantor-Beseitigung
    Allquantor-Einführung
    see Regel der Allquantor-Einführung
    Alternation
    see Disjunktion
    Annahme
    see Regel der Annahme
    Antecedens
    Formationsregeln
    Argument
    Grundbegriffe
    aussagenlogisch gültiges
    see semantischer Schlussbegriff
    gültiges
    see gültiges Argument
    ohne Prämissen
    Grundbegriffe
    prädikatenlogisch gültiges
    see semantischer Schlussbegriff
    semantisch gültiges
    see semantischer Schlussbegriff
    syntaktisch gültiges
    see syntaktischer Schlussbegriff
    arity (engl.)

    40. Fußnoten
    gerhard gentzen und Stanisaw
    http://logik.phl.univie.ac.at/~chris/skriptum/footnode.html
    ... betrachtet.
    Für eine exakte Definition bitte ich die Leserin, auf Kapitel (Seite ) zu warten.
    ... Schließen
    Kalküle des natürlichen Schließens sind auch als ,,Gentzen style calculi`` oder ,,Jaskowsky style calculi`` bekannt; Gerhard Gentzen und Stanisaw Jaskowsky erfanden unabhängig voneinander diese Art von Kalkülen und publizierten ihre Arbeiten 1934. Jan Wolenski zufolge stammen Jaskowskys Ergebnisse allerdings bereits aus dem Jahre 1927. Vgl. Gerhard Gentzen: ,,Untersuchungen über das logische Schließen``, in: Mathematische Zeitschrift 39 , 1934-1935, nachgedruckt in: Karel Berka/Lothar Kreiser: Logik-Texte. Kommentierte Auswahl zur Geschichte der modernen Logik , Berlin: Akademie 1986; Stanisaw Jaskowsky: ,,On the Rules of Suppositions in Formal Logic``, Warschau: 1934.
    ... Oder)
    Achtung: Der senkrechte Strich, ,, ``, wird häufiger für den Sheffer-Operator (,,NAND``) verwendet.
    ... ,,Tilde``
    Das Zeichen ,, heißt ,,Tilde``.
    ... Bedingung``)
    Das Konditional wird auch ,,materiale Implikation`` genannt und wird allzu oft als ,,impliziert`` gelesen. Diese Lesart ist nicht wirklich korrekt.

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