Cut-free Calculi for Challenge Logics in a Lazy Way

The development of cut-free calculi for expressive logics, e.g. quantified non-classical logics, is usually a non-trivial task. However, for a wide range of challenge logics there exists an elegant and uniform solution: By modeling and studying these logics as fragments of classical higher-order logic (HOL) [1, 4] — a research direction I have recently proposed [3] — existing results for HOL can often be reused. We illustrate the idea with quantified conditional logics [7].