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Sequent calculus in natural deduction style

  • Sara Negri (a1) and Jan von Plato (a2)
Abstract.
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.

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[2001a] von Plato J., Natural deduction with general elimination rules, Archive for Mathematical Logic, vol. 40 (2001), in press.
[2001b] Prawitz D., A proof of Gentzen's Hauptsatz without multicut, Archive for Mathematical Logic, vol. 40 (2001), pp. 918.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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