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Sequentialization for N-Graphs via Sub-N-Graphs

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Logic, Language, Information, and Computation (WoLLIC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8652))

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Abstract

Since proof-nets for MLL − were introduced by Girard (1987), several studies have been made on 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. This paper extends these studies to obtain a proof of sequentialization theorem for N-Graphs, which is a symmetric natural deduction calculus for classical propositional logic that adopts Danos–Regnier’s criteria and has defocussing switchable links, via sub-N-Graphs.

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Author information

Authors and Affiliations

  1. Depto. de Estatística e Informática, Universidade Federal Rural de Pernambuco, 52171-900, Recife, Pernambuco, Brazil

    Ruan Carvalho

  2. Centro de Informática, Universidade Federal de Pernambuco, 50740-560, Recife, Pernambuco, Brazil

    Laís Andrade, Anjolina de Oliveira & Ruy de Queiroz

Authors
  1. Ruan Carvalho
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  2. Laís Andrade
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  3. Anjolina de Oliveira
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  4. Ruy de Queiroz
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik, TU Darmstadt, Schlossgartenstrasse 7, 64289, Darmstadt, Germany

    Ulrich Kohlenbach

  2. Department of Computer Science, Universidad de Chile, Avenida Blanco Encalada 2120, Oficina 316, Tercer Piso, Santiago, Chile

    Pablo Barceló

  3. Centro de Informática, Universidade Federal de Pernambuco (UFPE), Av. Jornalista Anibal Fernandes, s/n, Cidade Universitária, 50., 740-560, Recife, PE, Brazil

    Ruy de Queiroz

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Carvalho, R., Andrade, L., de Oliveira, A., de Queiroz, R. (2014). Sequentialization for N-Graphs via Sub-N-Graphs. In: Kohlenbach, U., Barceló, P., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2014. Lecture Notes in Computer Science, vol 8652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44145-9_7

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  • DOI: https://doi.org/10.1007/978-3-662-44145-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44144-2

  • Online ISBN: 978-3-662-44145-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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