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Sequent calculus in natural deduction style

Published online by Cambridge University Press:  12 March 2014

Sara Negri
Affiliation:
University of Helsinki, Department of Philosophy, Helsinki, Finland, E-Mail: negri@helsinki.fi
Jan von Plato
Affiliation:
University of Helsinki, Department of Philosophy, Helsinki, Finland, E-Mail: vonplato@helsinki.fi
Corresponding

Abstract.

A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. A comparison to natural deduction is given through translation of derivations between the two systems. It is proved that if a cut formula is never principal in a derivation leading to the right premiss of cut, it is a subformula of the conclusion. Therefore it is sufficient to eliminate those cuts that correspond to detour and permutation conversions in natural deduction.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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