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arXiv · 1803.00555

Sequentialization for full N-Graphs via sub-N-Graphs

Ruan V. B. Carvalho·Lais S. Andrade·Anjolina G. de Oliveira·Ruy J. G. B. de Queiroz
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Abstract

Since proof-nets for MLL- were introduced by Girard (1987), several studies have appeared dealing with its soundness proof. Bellin & Van de Wiele (1995) produced an elegant proof based on properties of subnets (empires and kingdoms) and Robinson (2003) proposed a straightforward generalization of this presentation for proof-nets from sequent calculus for classical logic. In 2014 it was presented an extension of these studies to obtain a proof of the sequentialization theorem for the fragment of N-Graphs with conjunction, disjunction and negation connectives, via the notion of sub-N-Graphs. N-Graphs is a symmetric natural deduction calculus with multiple conclusions that adopts Danos-Regnier's criterion and has defocussing switchable links. In this paper, we present a sequentization for full propositional classical N-Graphs, showing how to find a split node in the middle of the proof even with a global rule for discharging hypothesis.

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Ruan V. B. Carvalho, Lais S. Andrade, Anjolina G. de Oliveira, Ruy J. G. B. de Queiroz. 2018-03-01. Sequentialization for full N-Graphs via sub-N-Graphs. https://arxiv.org/abs/1803.00555

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