CERES in higher-order logic

Annals of Pure and Applied Logic 162 (12):1001-1034 (2011)

We define a generalization of the first-order cut-elimination method CERES to higher-order logic. At the core of lies the computation of an set of sequents from a proof π of a sequent S. A refutation of in a higher-order resolution calculus can be used to transform cut-free parts of π into a cut-free proof of S. An example illustrates the method and shows that can produce meaningful cut-free proofs in mathematics that traditional cut-elimination methods cannot reach.
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DOI 10.1016/j.apal.2011.06.005
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References found in this work BETA

A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
Intensional Models for the Theory of Types.Reinhard Muskens - 2007 - Journal of Symbolic Logic 72 (1):98-118.
Resolution in Type Theory.Peter B. Andrews - 1971 - Journal of Symbolic Logic 36 (3):414-432.

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Ceres in Intuitionistic Logic.David Cerna, Alexander Leitsch, Giselle Reis & Simon Wolfsteiner - 2017 - Annals of Pure and Applied Logic 168 (10):1783-1836.

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