Abstract
In this paper we investigate, for intuitionistic implicational logic, the relationship between normalization in natural deduction and cut-elimination in a standard sequent calculus. First we identify a subset of proofs in the sequent calculus that correspond to proofs in natural deduction. Then we define a reduction relation on those proofs that exactly corresponds to normalization in natural deduction. The reduction relation is simulated soundly and completely by a cut-elimination procedure which consists of local proof transformations. It follows that the sequent calculus with our cut-elimination procedure is a proper extension that is conservative over natural deduction with normalization.
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Kikuchi, K. (2006). On a Local-Step Cut-Elimination Procedure for the Intuitionistic Sequent Calculus. In: Hermann, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2006. Lecture Notes in Computer Science(), vol 4246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11916277_9
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DOI: https://doi.org/10.1007/11916277_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-48281-9
Online ISBN: 978-3-540-48282-6
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