Cut-Simulation and Impredicativity

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Benzmueller, Christoph
Brown, Chad E.
Kohlhase, Michael
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Abstract
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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.
Comment: 21 pages
Keywords
Computer Science - Logic in Computer Science, Computer Science - Artificial Intelligence, F.4.1, I.2.3
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