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  1.  70
    An ecumenical notion of entailment.Elaine Pimentel, Luiz Carlos Pereira & Valeria de Paiva - 2019 - Synthese 198 (S22):5391-5413.
    Much has been said about intuitionistic and classical logical systems since Gentzen’s seminal work. Recently, Prawitz and others have been discussing how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system. We call Prawitz’ proposal the Ecumenical System, following the terminology introduced by Pereira and Rodriguez. In this work we present an Ecumenical sequent calculus, as opposed to the original natural deduction version, and state some proof theoretical properties of the system. We reason that (...)
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  2.  35
    A Pure View of Ecumenical Modalities.Sonia Marin, Luiz Carlos Pereira, Elaine Pimentel & Emerson Sales - 2021 - In Alexandra Silva, Renata Wassermann & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation: 27th International Workshop, Wollic 2021, Virtual Event, October 5–8, 2021, Proceedings. Springer Verlag. pp. 388-407.
    Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion on proof systems for combining logics. This discussion has been extended to alethic modalities using Simpson’s meta-logical characterization: necessity is independent of the viewer, while possibility can be either intuitionistic or classical. In this work, we propose a pure, label free calculus for ecumenical modalities, nEK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {nEK}$$\end{document}, where exactly one logical operator figures (...)
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  3.  20
    From axioms to synthetic inference rules via focusing.Sonia Marin, Dale Miller, Elaine Pimentel & Marco Volpe - 2022 - Annals of Pure and Applied Logic 173 (5):103091.
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  4.  6
    Translations and Prawitz’s Ecumenical System.Luiz Carlos Pereira, Elaine Pimentel & Valeria de Paiva - forthcoming - Studia Logica:1-16.
    Since Prawitz proposal of his ecumenical system, where classical and intuitionistic logics co-exist in peace, there has been a discussion about the relation between translations and the ecumenical perspective. While it is undeniable that there exists a relationship, it is also undeniable that its very nature is controversial. The aim of this paper is to show that there are interesting relations between the Gödel-Gentzen translation and the ecumenical perspective. We show that the ecumenical perspective cannot be reduced to the Gödel-Gentzen (...)
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  5. The ILLTP Library for Intuitionistic Linear Logic.Carlos Olarte, Valeria Correa Vaz De Paiva, Elaine Pimentel & Giselle Reis - manuscript
    Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this work we propose a library for benchmarking Girard's (propositional) intuitionistic linear logic. For a quick bootstrapping of the collection of problems, and for discussing the selection of relevant problems and understanding their meaning as linear logic theorems, we use translations of the collection of Kleene's intuitionistic theorems in the (...)
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  6.  13
    On an Ecumenical Natural Deduction with Stoup. Part I: The Propositional Case.Luiz Carlos Pereira & Elaine Pimentel - 2024 - In Antonio Piccolomini D'Aragona (ed.), Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction. Springer Verlag. pp. 139-169.
    In 2015 Dag Prawitz proposed a natural deduction ecumenical system, where classical logic and intuitionistic logic are codified in the same system. In his ecumenical system, Prawitz recovers the harmony of rules, but the rules for the classical operators do not satisfy separability. In fact, the classical rules are not pure, in the sense that negation is used in the definition of the introduction and elimination rules for the classical operators. In this work we propose an ecumenical system adapting, to (...)
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