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Main Articles

On Inversion Principles

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Pages 103-113 | Received 10 May 2007, Accepted 31 Aug 2007, Published online: 30 Apr 2008

References

  • Gentzen , G. 1935 . ‘Untersuchungen über das logische Schliessen I, II’ . Mathematische Zeitschrift , 39 : 176 – 210 . Eng. tran. in [Sza69]
  • Hermes , H. 1959 . “ ‘Zum Inversionsprinzip der operativen Logik’ ” . In Constructivity in Mathematics , Edited by: Heyting , A. Amsterdam : North-Holland Publ. Co. .
  • Lorenzen , P. 1950 . ‘Konstruktive Begründung der Mathematik’ . Mathematische Zeitschrift , 53 : 162 – 202 .
  • Lorenzen , P. 1955 . Einfürung in die operative Logik und Mathematik , Berlin-Güttingen-Heidelberg : Springer .
  • Negri , S. 2002 . ‘Varieties of linear calculi’ . Journal of Philosophical Logic , 31 : 569 – 590 .
  • Negri , S. and von Plato , J. 2001 . Structural Proof Theory , Cambridge : Cambridge University Press .
  • Prawitz , D. 1965 . Natural Deduction. A Proof-Theoretical Study , Stockholm : Almkvist & Wiksell .
  • Prawitz , D. . ‘Ideas and results in proof theory’ . Proceedings of the Second Scandinavian Logic Symposium . Edited by: Fenstad , J. E. Amsterdam : North-Holland Publ. Co. .
  • Prawitz , D. 1979 . “ ‘Proofs and the meaning and completeness of the logical constants’ ” . In Essays on Mathematical and Philosophical Logic , Reidel : Dordrecht .
  • Prior , A. 1960–1961 . ‘The runabout inference ticket’ . Analysis , 21 : 38 – 39 .
  • Read , S. 2000 . ‘Harmony and autonomy in classical logic’ . Journal of Philosophical Logic , 29 : 123 – 154 .
  • Schroeder-Heister , P. “ ‘Operative logic and proof-theoretic semantics’ ” . In Advances in Natural Deduction Volume under review
  • Schroeder-Heister , P. 1982 . ‘Logische Konstanten und Regeln. Zur Deutung von Aussagenoperatoren’ . Conceptus , 16 : 45 – 60 .
  • Schroeder-Heister , P. 1984 . ‘A natural extension of natural deduction’ . The Journal of Symbolic Logic , 49 : 1284 – 1300 .
  • Schroeder-Heister , P. 2007 . ‘Generalized Definitional Reflection and the Inversion Principle’ . Logica Universalis , 1 : 355 – 376 .
  • Schroeder-Heister , P. “ ‘Lorenzens operative Logik und moderne beweistheorethische Semantik’ ” . In Der Konstruktivismus in der Philosophie im Ausgang von Wilhelm Kamlah und Paul Lorenzen , Edited by: Mittelstraß , J. Paderborn : Mentis . In press
  • Szabo M. E. 1969 The Collected Papers of Gerhardt Gentzen Amsterdam North-Holland Publ. Co.
  • Tesconi, L. ‘A failure of correspondence between normalization and cut-elimination’, Submitted for publication
  • von Plato , J. 2003 . ‘Rereading Gentzen’ . Synthese , 173 : 195 – 209 .

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