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A Semantical View of Proof Systems

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Logic, Language, Information, and Computation (WoLLIC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10944))

Abstract

In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a semantical characterisation of intuitionistic, normal and non-normal modal logics for all these systems, via a case-by-case translation between labelled nested to labelled sequent systems.

E. Pimentel—Funded by CNPq, CAPES and the project FWF START Y544-N23.

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Notes

  1. 1.

    All over this text, we will use n as a superscript, etc for indicating “nested”. Hence e.g., \(\rightarrow _R^n\) will be the designation of the implication right rule in the nesting framework.

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Author information

Authors and Affiliations

  1. Departamento de Matemática, UFRN, Natal, Brazil

    Elaine Pimentel

Authors
  1. Elaine Pimentel
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Correspondence to Elaine Pimentel .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, Indiana, USA

    Lawrence S. Moss

  2. Centro de Informática, Univ Federal de Pernambuco (UFPE), Recife, Pernambuco, Brazil

    Ruy de Queiroz

  3. Universidad de los Andes, Bogotá, Colombia

    Maricarmen Martinez

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Pimentel, E. (2018). A Semantical View of Proof Systems. In: Moss, L., de Queiroz, R., Martinez, M. (eds) Logic, Language, Information, and Computation. WoLLIC 2018. Lecture Notes in Computer Science(), vol 10944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-57669-4_3

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  • DOI: https://doi.org/10.1007/978-3-662-57669-4_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-57668-7

  • Online ISBN: 978-3-662-57669-4

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