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Cut Elimination in the Presence of Axioms

Published online by Cambridge University Press:  15 January 2014

Sara Negri  and
Jan von Plato
Sara Negri
Affiliation:
Department of Philosophy, University of Helsinki, Helsinki, FinlandE-mail: negri@helsinki.fi
Jan von Plato
Affiliation:
Department of Philosophy, University of Helsinki, Helsinki, FinlandE-mail: vonplato@helsinki.fi
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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.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 4 , Issue 4 , December 1998 , pp. 418 - 435
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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