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arXiv · 0902.0043

Cut-Simulation and Impredicativity

Christoph Benzmueller·Chad E. Brown·Michael Kohlhase
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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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Christoph Benzmueller, Chad E. Brown, Michael Kohlhase. 2009-01-31. Cut-Simulation and Impredicativity. https://doi.org/10.2168/lmcs-5(1:6)2009

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