License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2023.3
URN: urn:nbn:de:0030-drops-188003
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18800/
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Pimentel, Elaine ; Pereira, Luiz Carlos

A Tour on Ecumenical Systems (Invited Talk)

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LIPIcs-CALCO-2023-3.pdf (0.8 MB)

Abstract

Ecumenism can be understood as a pursuit of unity, where diverse thoughts, ideas, or points of view coexist harmoniously. In logic, ecumenical systems refer, in a broad sense, to proof systems for combining logics. One captivating area of research over the past few decades has been the exploration of seamlessly merging classical and intuitionistic connectives, allowing them to coexist peacefully. In this paper, we will embark on a journey through ecumenical systems, drawing inspiration from Prawitz' seminal work [Dag Prawitz, 2015]. We will begin by elucidating Prawitz' concept of "ecumenism" and present a pure sequent calculus version of his system. Building upon this foundation, we will expand our discussion to incorporate alethic modalities, leveraging Simpson’s meta-logical characterization. This will enable us to propose several proof systems for ecumenical modal logics. We will conclude our tour with some discussion towards a term calculus proposal for the implicational propositional fragment of the ecumenical logic, the quest of automation using a framework based in rewriting logic, and an ecumenical view of proof-theoretic semantics.

BibTeX - Entry

@InProceedings{pimentel_et_al:LIPIcs.CALCO.2023.3,
  author =	{Pimentel, Elaine and Pereira, Luiz Carlos},
  title =	{{A Tour on Ecumenical Systems}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18800},
  URN =		{urn:nbn:de:0030-drops-188003},
  doi =		{10.4230/LIPIcs.CALCO.2023.3},
  annote =	{Keywords: Intuitionistic logic, classical logic, modal logic, ecumenical systems, proof theory}
}

Keywords: Intuitionistic logic, classical logic, modal logic, ecumenical systems, proof theory
Collection: 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)
Issue Date: 2023
Date of publication: 02.09.2023

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