Authors
Mirjana Borisavljević
University of Belgrade
Abstract
In derivations of a sequent system, $\mathcal{L}\mathcal{J}$, and a natural deduction system, $\mathcal{N}\mathcal{J}$, the trails of formulae and the subformula property based on these trails will be defined. The derivations of $\mathcal{N}\mathcal{J}$ and $\mathcal{L}\mathcal{J}$ will be connected by the map $g$, and it will be proved the following: an $\mathcal{N}\mathcal{J}$-derivation is normal $\Longleftrightarrow$, it has the subformula property based on trails $\Longleftrightarrow$, its $g$-image in $\mathcal{L}\mathcal{J}$ is without maximum cuts $\Longrightarrow$ that $g$-image has the subformula property based on trails. In $\mathcal{L}\mathcal{J}$-derivations, another type of cuts, sub-cuts, will be introduced, and it will be proved the following: all cuts of an $\mathcal{L}\mathcal{J}$-derivation are sub-cuts $\Longleftrightarrow$, it has the subformula property based on trails.
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DOI 10.1093/jigpal/jzaa017
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References found in this work BETA

Gentzen's Proof of Normalization for Natural Deduction.Jan von Plato - 2008 - Bulletin of Symbolic Logic 14 (2):240-257.
Gentzen's Proof of Normalization for Natural Deduction.Jan von Plato & G. Gentzen - 2008 - Bulletin of Symbolic Logic 14 (2):240 - 257.

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