Abstract
The paper discusses the relationship between normal natural deductions and cutfree proofs in Gentzen (sequent) calculi in the absence of term labeling. For Gentzen calculi this is the usual version; for natural deduction this is the version under the complete discharge convention, where open assumptions are always discharged as soon as possible. The paper supplements work by Mints, Pinto, Dyckhoff, and Schwichtenberg on the labeled calculi.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Gentzen, ‘Untersuchungen über das logische Schliessen I,II’, Mathematische Zeitschrift 39:176–210, 405–431, 1935. Translation in [Gen69], 68–131.
G. Gentzen, The Collected Papers of Gerhard Gentzen, North-Holland Publ. Co., Amsterdam, 1969. English translation of Gentzen's papers, edited and introduced by M. E. Szabo.
H. Herbelin, ‘A Λ-calculus structure isomorphic to Gentzen-style sequent calculus structure’, in L. Pacholski and J. Tiuryn, editors, Computer Science Logic. 8th Workshop, CSL'94. Kazimierz, Poland, September 1994, Lecture Notes in Computer Science 933, pages 61–75, Springer-Verlag, Berlin, Heidelberg, New York, 1995.
W. A. Howard, ‘The formulae-as-types notion of construction’, in [SH80], pages 480–490, 1980. Circulated as preprint since 1969.
S. JaŚkowski, ‘On the rules of supposition in formal logic’ (Polish), Studia Logica (old series) 1:5–32, 1934. Translation Polish Logic 1920–1939, S. McCall, ed., Clarendon Press, Oxford, 1967, 232–258.
D. Leivant, ‘Assumption classes in natural deduction’, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 25:1–4, 1979.
G. E. Mints, ‘Normal forms for sequent derivations’, in P. Odifreddi, editor, Kreiseliana, pages 469–492, A. K. Peters, Wellesley, Mass., 1996.
D. Prawitz, Natural deduction. A Proof-theoretical Study, Almquist and Wiksell, Stockholm, 1965.
H. Schwichtenberg, ‘Termination of permutative conversions in intuitionistic Gentzen calculi’, 1997. Draft from June 2, 1997, 11 pages.
J. P. Seldin and J. R. Hindley, editors, To H. B. Curry: Essays on Combinatory logic, Lambda Calculus and Formalism, Academic Press, New York, 1980.
A. S. Troelstra and H. Sshwichtenberg, Basic Proof Theory, Cambridge University Press, Cambridge U.K., 1996.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Troelstra, A.S. Marginalia on Sequent Calculi. Studia Logica 62, 291–303 (1999). https://doi.org/10.1023/A:1026413320413
Issue Date:
DOI: https://doi.org/10.1023/A:1026413320413