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  1. (1 other version)Proof-Theoretic Semantics.Peter Schroeder-Heister - 2024 - Stanford Encyclopedia of Philosophy.
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  • Intuitionistic Modal Algebras.Sergio A. Celani & Umberto Rivieccio - 2024 - Studia Logica 112 (3):611-660.
    Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...)
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  • On Combining Intuitionistic and S4 Modal Logic.João Rasga & Cristina Sernadas - 2024 - Bulletin of the Section of Logic 53 (3):321-344.
    We address the problem of combining intuitionistic and S4 modal logic in a non-collapsing way inspired by the recent works in combining intuitionistic and classical logic. The combined language includes the shared constructors of both logics namely conjunction, disjunction and falsum as well as the intuitionistic implication, the classical implication and the necessity modality. We present a Gentzen calculus for the combined logic defined over a Gentzen calculus for the host S4 modal logic. The semantics is provided by Kripke structures. (...)
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  • 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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  • Combining Intuitionistic and Classical Propositional Logic: Gentzenization and Craig Interpolation.Masanobu Toyooka & Katsuhiko Sano - 2024 - Studia Logica 112 (5):1091-1121.
    This paper studies a combined system of intuitionistic and classical propositional logic from proof-theoretic viewpoints. Based on the semantic treatment of Humberstone (J Philos Log 8:171–196, 1979) and del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996), a sequent calculus \(\textsf{G}(\textbf{C}+\textbf{J})\) is proposed. An approximate idea of obtaining \(\textsf{G}(\textbf{C}+\textbf{J})\) is adding rules for classical implication on top of the intuitionistic multi-succedent sequent calculus by Maehara (Nagoya Math J 7:45–64, 1954). However, in the semantic treatment, some formulas do not (...)
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  • Towards logical foundations for probabilistic computation.Melissa Antonelli, Ugo Dal Lago & Paolo Pistone - 2024 - Annals of Pure and Applied Logic 175 (9):103341.
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  • Ecumenical Propositional Tableau.Renato Leme, Marcelo Coniglio, Bruno Lopes & Giorgio Venturi - forthcoming - Studia Logica:1-28.
    Ecumenical logic aims to peacefully join classical and intuitionistic logic systems, allowing for reasoning about both classical and intuitionistic statements. This paper presents a semantic tableau for propositional ecumenical logic and proves its soundness and completeness concerning Ecumenical Kripke models. We introduce the Ecumenical Propositional Tableau ( $$E_T$$ ) and demonstrate its effectiveness in handling mixed statements.
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