Cut elimination in the presence of axioms

Bulletin of Symbolic Logic 4 (4):418-435 (1998)
Abstract
A way is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also the rules of weakening and contraction can be eliminated. Applications include a system of predicate logic with equality in which also cuts on the equality axioms are eliminated
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Sara Negri (2011). Proof Theory for Modal Logic. Philosophy Compass 6 (8):523-538.

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