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

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 o...

Full description

Saved in:
Bibliographic Details
Main Authors Carvalho, Ruan V. B, Andrade, Lais S, de Oliveira, Anjolina G, de Queiroz, Ruy J. G. B
Format Journal Article
LanguageEnglish
Published 01.03.2018
Subjects
Computer Science - Logic in Computer Science
Online AccessGet full text

Cover

More Information
Summary: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.
DOI:10.48550/arxiv.1803.00555