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  1. A Method of Generating Modal Logics Defining Jaśkowski’s Discussive Logic D2.Marek Nasieniewski & Andrzej Pietruszczak - 2011 - Studia Logica 97 (1):161-182.
    Jaśkowski’s discussive logic D2 was formulated with the help of the modal logic S5 as follows (see [7, 8]): \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \in {D_{2}}}$$\end{document} iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}$$\end{document}, where (–)• is a translation of discussive formulae from Ford into the modal language. We say that a modal logic L defines D2 iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm D}_{2} = (...)
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  • Topics in the Proof Theory of Non-classical Logics. Philosophy and Applications.Fabio De Martin Polo - 2023 - Dissertation, Ruhr-Universität Bochum
    Chapter 1 constitutes an introduction to Gentzen calculi from two perspectives, logical and philosophical. It introduces the notion of generalisations of Gentzen sequent calculus and the discussion on properties that characterize good inferential systems. Among the variety of Gentzen-style sequent calculi, I divide them in two groups: syntactic and semantic generalisations. In the context of such a discussion, the inferentialist philosophy of the meaning of logical constants is introduced, and some potential objections – mainly concerning the choice of working with (...)
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  • On Paracomplete Versions of Jaśkowski's Discussive Logic.Krystyna Mruczek-Nasieniewska, Yaroslav Petrukhin & Vasily Shangin - 2024 - Bulletin of the Section of Logic 53 (1):29-61.
    Jaśkowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the modal logic S5 via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic D2p.
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  • A Method of Generating Modal Logics Defining Jaśkowski’s Discussive Logic D2.Marek Nasieniewski & Andrzej Pietruszczak - 2011 - Studia Logica 97 (1):161-182.
    Jaśkowski’s discussive logic D2 was formulated with the help of the modal logic S5 as follows (see [7, 8]): \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \in {D_{2}}}$$\end{document} iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}$$\end{document}, where (–)• is a translation of discussive formulae from Ford into the modal language. We say that a modal logic L defines D2 iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm D}_{2} = (...)
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  • A modal extension of Jaśkowski’s discussive logic $\textbf{D}_\textbf{2}$.Krystyna Mruczek-Nasieniewska, Marek Nasieniewski & Andrzej Pietruszczak - 2019 - Logic Journal of the IGPL 27 (4):451-477.
    In Jaśkowski’s model of discussion, discussive connectives represent certain interactions that can hold between debaters. However, it is not possible within the model for participants to use explicit modal operators. In the paper we present a modal extension of the discussive logic $\textbf{D}_{\textbf{2}}$ that formally corresponds to an extended version of Jaśkowski’s model of discussion that permits such a use. This logic is denoted by $\textbf{m}\textbf{D}_{\textbf{2}}$. We present philosophical motivations for the formulation of this logic. We also give syntactic characterizations (...)
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  • Axiomatizing a Minimal Discussive Logic.Oleg Grigoriev, Marek Nasieniewski, Krystyna Mruczek-Nasieniewska, Yaroslav Petrukhin & Vasily Shangin - 2023 - Studia Logica 111 (5):855-895.
    In the paper we analyse the problem of axiomatizing the minimal variant of discussive logic denoted as $$ {\textsf {D}}_{\textsf {0}}$$ D 0. Our aim is to give its axiomatization that would correspond to a known axiomatization of the original discussive logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2. The considered system is minimal in a class of discussive logics. It is defined similarly, as Jaśkowski’s logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2 but with the help of the deontic normal logic (...)
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  • Adjoint interpretations of sentential calculi.Tomasz Fukmanowski - 1982 - Studia Logica 41 (4):359 - 374.
    The aim of this paper is to give a general background and a uniform treatment of several notions of mutual interpretability. Sentential calculi are treated as preorders and logical invariants of adjoint situations, i.e. Galois connections are investigated. The class of all sentential calculi is treated as a quasiordered class.Some methods of the axiomatization of the M-counterparts of modal systems are based on particular adjoints. Also, invariants concerning adjoints for calculi with implication are pointed out. Finally, the notion of interpretability (...)
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  • On Jaśkowski's Discussive Logics.Newton C. A. da Costa & Francisco A. Doria - 1995 - Studia Logica 54 (1):33 - 60.
    We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.
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  • On Ja?kowski's discussive logics.Newton C. A. Costa & Francisco A. Doria - 1995 - Studia Logica 54 (1):33-60.
    We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.
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  • Rough Consequence and other Modal Logics.Martin Bunder - 2015 - Australasian Journal of Logic 12 (1).
    Chakraborty and Banerjee have introduced a rough consequence logic based on the modal logic S5. This paper shows that rough consequence logics, with many of the same properties, can be based on modal logics as weak as K, with a simpler formulation than that of Chakraborty and Banerjee. Also provided are decision procedures for the rough consequence logics and equivalences and independence relations between various systems S and the rough consequence logics, based on them. It also shows that each logic, (...)
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  • Modal logics connected with systems S4n of Sobociński.Jerzy J. Blaszczuk & Wieslaw Dziobiak - 1977 - Studia Logica 36 (3):151-164.
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  • Wittgenstein on Incompleteness Makes Paraconsistent Sense.Francesco Berto - 2008 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 257--276.
    I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...)
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  • Some paraconsistent sentential calculi.Jerzy J. Błaszczuk - 1984 - Studia Logica 43 (1-2):51 - 61.
    In [8] Jakowski defined by means of an appropriate interpretation a paraconsistent calculusD 2 . In [9] J. Kotas showed thatD 2 is equivalent to the calculusM(S5) whose theses are exactly all formulasa such thatMa is a thesis ofS5. The papers [11], [7], [3], and [4] showed that interesting paraconsistent calculi could be obtained using modal systems other thanS5 and modalities other thanM. This paper generalises the above work. LetA be an arbitrary modality (i.e. string ofM''s,L''s and negation signs). Then (...)
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  • Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
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  • On Modal Logics Defining Jaśkowski's D2-Consequence.Marek Nasieniewski & Andrzej Pietruszczak - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 141--161.
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