Abstract
We prove confluence of two cut-elimination procedures for the implicational fragment of a standard intuitionistic sequent calculus. One of the cut-elimination procedures uses global proof transformations while the other consists of local ones. Both of them include permutation of cuts to simulate β-reduction in an isomorphic image of the λ-calculus. We establish the confluence properties through a conservativity result on the cut-elimination procedures.
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Bloo, R., Geuvers, H.: Explicit substitution: On the edge of strong normalization. Theoretical Computer Science 211, 375–395 (1999)
Danos, V., Joinet, J.-B., Schellinx, H.: A new deconstructive logic: Linear logic. The Journal of Symbolic Logic 62, 755–807 (1997)
Espírito Santo, J.: Revisiting the correspondence between cut elimination and normalisation. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 600–611. Springer, Heidelberg (2000)
Gentzen, G.: Untersuchungen über das logische Schliessen. Mathematische Zeitschrift, 39: pp. 176–210, pp. 405–431, English translation in [9 pp. 68–131] (1935)
Girard, J.-Y.: Linear logic. Theoretical Computer Science 50, 1–102 (1987)
Hardin, T.: Résultats de confluence pour les règles fortes de la logique combinatoire catégorique et liens avec les lambda-calculs. Thèse de doctorat, Université de Paris VII (1987)
Howard, W.A.: The formulae-as-types notion of construction. In: Seldin, J.P., Hindley, J.R. (eds.) To H. B. Curry: Essays on Combinatory Logic, Lambda-Calculus and Formalism, pp. 479–490. Academic Press, San Diego (1980)
Kikuchi, K.: On a local-step cut-elimination procedure for the intuitionistic sequent calculus. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 120–134. Springer, Heidelberg (2006)
Szabo, M.E. (ed.): The Collected Papers of Gerhard Gentzen. North-Holland, Amsterdam (1969)
Takahashi, M.: Parallel reductions in λ-calculus. Information and Computation 118, 120–127 (1995)
Urban, C., Bierman, G.M.: Strong normalisation of cut-elimination in classical logic. Fundamenta Informaticae 45, 123–155 (2001)
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Kikuchi, K. (2007). Confluence of Cut-Elimination Procedures for the Intuitionistic Sequent Calculus. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_41
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DOI: https://doi.org/10.1007/978-3-540-73001-9_41
Publisher Name: Springer, Berlin, Heidelberg
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