Abstract
We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic — in our case a sequent calculus for classical type theory — is like adding cut. The phenomenon equally applies to prominent axioms like Boolean- and functional extensionality, induction, choice, and description. This calls for the development of calculi where these principles are built-in instead of being treated axiomatically.
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Benzmüller, C.E., Brown, C.E., Kohlhase, M. (2006). Cut-Simulation in Impredicative Logics. 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_20
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DOI: https://doi.org/10.1007/11814771_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37187-8
Online ISBN: 978-3-540-37188-5
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