CERES in higher-order logic
Stefan Hetzl, Alexander Leitsch, Daniel S. Weller · Annals of Pure and Applied Logic · 2011
We define a generalization CERESω of the first-order cut-elimination method CERES to higher-order logic. At the core of CERESω lies the computation of an (unsatisfiable) set of sequents CS(π) (the characteristic sequent set) from a proof π of a sequent S. A refutation of CS(π) in a higher-order resolution calculus can be used to transform cut-free parts of π (the proof projections) into a cut-free proof of S. An example illustrates the method and shows that CERESω can produce meaningful cut-free proofs in mathematics that traditional cut-elimination methods cannot reach.