Abstract
Inspired by the Curry-Howard correspondence, we study normalisation procedures in the depth-bounded intuitionistic sequent calculus of Hudelmaier (1988) for the implicational case, thus strengthening existing approaches to Cut-admissibility. We decorate proofs with terms and introduce various term-reduction systems representing proof transformations. In contrast to previous papers which gave different arguments for Cut-admissibility suggesting weakly normalising procedures for Cut-elimination, our main reduction system and all its variations are strongly normalising, with the variations corresponding to different optimisations, some of them with good properties such as confluence.
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Dyckhoff, R., Kesner, D., Lengrand, S. (2006). Strong Cut-Elimination Systems for Hudelmaier’s Depth-Bounded Sequent Calculus for Implicational Logic. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_31
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DOI: https://doi.org/10.1007/11814771_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37187-8
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