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On Paracomplete Versions of Jaśkowski's Discussive Logic

dc.contributor.authorMruczek-Nasieniewska, Krystyna
dc.contributor.authorPetrukhin, Yaroslav
dc.contributor.authorShangin, Vasily
dc.date.accessioned2024-04-12T09:57:38Z
dc.date.available2024-04-12T09:57:38Z
dc.date.issued2024-01-04
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/51686
dc.description.abstractJaśkowski'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.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;1en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectdiscussive logicen
dc.subjectdiscursive logicen
dc.subjectmodal logicen
dc.subjectparacomplete logicen
dc.subjectparaconsistent logicen
dc.titleOn Paracomplete Versions of Jaśkowski's Discussive Logicen
dc.typeOther
dc.page.number29-61
dc.contributor.authorAffiliationMruczek-Nasieniewska, Krystyna - Nicolaus Copernicus University in Toruń, Department of Logic, Institute of Philsophy, Faculty of Philosophy and Social Sciencesen
dc.contributor.authorAffiliationPetrukhin, Yaroslav - University of Łódź, Department of Logic, Institute of Philosophy, Faculty of History and Philosophyen
dc.contributor.authorAffiliationShangin, Vasily - Lomonosov Moscow State University, Department of Logic, Faculty of Philosophyen
dc.identifier.eissn2449-836X
dc.referencesG. Achtelik, L. Dubikajtis, E. Dudek, J. Konior, On independence of axioms of Jaśkowski’s discussive propositional calculus, Reports on Mathematical Logic, vol. 11 (1981), pp. 3–11.en
dc.referencesS. Akama, J. M. Abe, K. Nakamatsu, Constructive discursive logic with strong negation, Logique et Analyse. Nouvelle Série, vol. 54(215) (2011), pp. 395–408, URL: https://www.jstor.org/stable/44085016en
dc.referencesS. Akama, N. C. A. da Costa, Why paraconsistent logics?, [in:] S. Akama (ed.), Towards paraconsistent engineering, vol. 110 of Intelligent Systems Reference Library, Springer, Cham (2016), pp. 7–24, DOI: https://doi.org/10.1007/978-3-319-40418-9_2en
dc.referencesA. Almukdad, D. Nelson, Constructible falsity and inexact predicates, The Journal of Symbolic Logic, vol. 49(1) (1984), pp. 231–233, DOI: https://doi.org/10.2307/2274105en
dc.referencesA. R. Anderson, N. D. Belnap, Jr., Entailment: The Logic of Relevance and Necessity, Volume 1, Princeton University Press, Princeton, N.J.-London (1975).en
dc.referencesO. Arieli, A. Avron, Four-valued paradefinite logics, Studia Logica, vol. 105(6) (2017), pp. 1087–1122, DOI: https://doi.org/10.1007/s11225-017-9721-4en
dc.referencesA. Avron, Paraconsistent fuzzy logic preserving non-falsity, Fuzzy Sets and Systems, vol. 292 (2016), pp. 75–84, DOI: https://doi.org/10.1016/j.fss.2014.07.001en
dc.referencesR. Ballarin, Modern Origins of Modal Logic, [in:] E. N. Zalta, U. Nodelman (eds.), The Stanford Encyclopedia of Philosophy, Fall 2023 ed., Metaphysics Research Lab, Stanford University (2023), URL: https://plato.stanford.edu/archives/fall2023/entries/logic-modal-origins/en
dc.referencesJ.-Y. Béziau, The Future of Paraconsistent Logics, Logical Studies, vol. 2 (1999), pp. 1–28, URL: http://wwwa.unine.ch/unilog/jyb/future-pl.pdfen
dc.referencesD. A. Bochvar, On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus, History and Philosophy of Logic, vol. 2 (1981), pp. 87–112, DOI: https://doi.org/10.1080/01445348108837023 translated from the Russian by Merrie Bergmann.en
dc.referencesJ. Ciuciura, A quasi-discursive system ND₂⁺, Notre Dame Journal of Formal Logic, vol. 47(3) (2006), pp. 371–384, DOI: https://doi.org/10.1305/ndjfl/1163775444en
dc.referencesJ. Ciuciura, Frontiers of the discursive logic, Bulletin of the Section of Logic, vol. 37(2) (2008), pp. 81–92.en
dc.referencesJ. Ciuciura, Non-adjunctive discursive logic, Bulletin of the Section of Logic, vol. 42(3-4) (2013), pp. 169–181, DOI: https://doi.org/10.1007/bf03322857en
dc.referencesN. da Costa, L. Dubikajtis, On Jaśkowski’s Discussive Logic, [in:] A. I. Arruda, N. C. A. da Costa, R. Chuaqui (eds.), Non-Classical Logics, Model Theory, And Computability, vol. 89 of Studies in Logic and the Foundations of Mathematics, Elsevier (1977), pp. 37–56, DOI: https://doi.org/10.1016/S0049-237X(08)70644-Xen
dc.referencesR. Ertola, F. Esteva, T. Flaminio, L. Godo, C. Noguera, Paraconsistency properties in degree-preserving fuzzy logics, Soft Computing, vol. 19(3) (2015), pp. 531–546, DOI: https://doi.org/10.1007/s00500-014-1489-0en
dc.referencesT. Furmanowski, Remarks on discussive propositional calculus, Studia Logica, vol. 34(1) (1975), pp. 39–43, DOI: https://doi.org/10.1007/BF02314422en
dc.referencesJ. W. Garson, Modal logic for philosophers, Cambridge University Press, Cambridge (2006), DOI: https://doi.org/10.1017/CBO9780511617737en
dc.referencesK. Gödel, Zum Intuitionistischen Aussagenkalkül, Anzeiger der Akademie der Wissenschaften in Wien, vol. 69 (1932), pp. 65–66.en
dc.referencesO. Grigoriev, M. Nasieniewski, K. Mruczek-Nasieniewska, Y. Petrukhin, V. Shangin, Axiomatizing a minimal discussive logic, Studia Logica, vol. 111(5) (2023), pp. 855–895, DOI: https://doi.org/10.1007/s11225-023-10042-9en
dc.referencesA. Heyting, Die formalen Regeln der intuitionistischen Logik, Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin (1930).en
dc.referencesS. Jaśkowski, Recherches sur le système de la logique intuitioniste, [in:] Actes du Congrès International de Philosophie Scientifique, VI Philosophie des mathématiques, Hermann & Cie, Paris (1936), pp. 58–61, (in: Actualités scientifiques et industrielles, vol. 393).en
dc.referencesS. Jaśkowski, On the discussive conjunction in the propositional calculus for inconsistent deductive systems, Logic and Logical Philosophy, vol. 7 (1999), pp. 57–59, DOI: https://doi.org/10.12775/llp.1999.004 translated by Jerzy Perzanowski from the Polish O koniunkcji dyskusyjnej w rachunku zdań dla systemów dedukcyjnych sprzecznych, Studia Societatis Scientiarum Torunensis. Sectio A, Mathematica-Physica, vol. 1(8) (1949), no. 8, 171–172.en
dc.referencesS. Jaśkowski, A propositional calculus for inconsistent deductive systems, Logic and Logical Philosophy, vol. 7 (1999), pp. 35–56, DOI: https://doi.org/10.12775/llp.1999.003 translated by Jerzy Perzanowski from the Polish Rachunek zdań dla systemow dedukcyjnych sprzecznych, Studia Societatis Scientiarum Torunensis. Sectio A, Mathematica-Physica, vol. 1(5) (1948), pp. 57–77; another English translation, by Olgierd Wojtasiewicz: Propositional calculus for contradictory deductive systems, Studia Logica, vol. 24 (1969), pp. 143–157.en
dc.referencesS. C. Kleene, An addendum, The Journal of Symbolic Logic, vol. 28 (1963), pp. 154–156, DOI: https://doi.org/10.2307/2271596en
dc.referencesA. Kolmogoroff, Zur Deutung der intuitionistischen Logik, Mathematische Zeitschrift, vol. 35(1) (1932), pp. 58–65, DOI: https://doi.org/10.1007/BF01186549en
dc.referencesJ. Kotas, The axiomatization of S. Jaśkowski’s discussive system, Studia Logica, vol. 33 (1974), pp. 195–200, DOI: https://doi.org/10.1007/BF02120494en
dc.referencesJ. Kotas, N. C. A. da Costa, On some Modal Logical Systems Defined in Connexion with Jaśakowski’s Problem, [in:] A. I. Arruda, N. C. A. da Costa, R. Chuaqui (eds.), Non-Classical Logics, Model Theory, And Computability, vol. 89 of Studies in Logic and the Foundations of Mathematics, Elsevier (1977), pp. 57–73, DOI: https://doi.org/10.1016/S0049-237X(08)70645-1en
dc.referencesS. Kovač, In what sense is Kantian principle of contradiction non-classical?, Logic and Logical Philosophy, vol. 17(3) (2008), pp. 251–274, DOI: https://doi.org/10.12775/LLP.2008.013en
dc.referencesA. Loparić, N. C. A. da Costa, Paraconsistency, paracompleteness, and valuations, Logique et Analyse. Nouvelle Série, vol. 27(106) (1984), pp. 119–131, URL: https://www.jstor.org/stable/44084079en
dc.referencesA. Loparić, N. C. A. da Costa, Paraconsistency, paracompleteness, and induction, Logique et Analyse. Nouvelle Série, vol. 29(113) (1986), pp. 73–80.en
dc.referencesJ. Łukasiewicz, On three-valued logic (in Polish), Ruch Filozoficzny, vol. 5 (1920), pp. 170–171, English translation: J. Łukasiewicz: Selected Works, L. Borkowski (ed.), Amsterdam, North-Holland Publishing Company (1970), pp. 87–88.en
dc.referencesK. Mruczek-Nasieniewska, M. Nasieniewski, A. Pietruszczak, A modal extension of Jaśkowski’s discussive logic D2, Logic Journal of the IGPL, vol. 27(4) (2019), pp. 451–477, DOI: https://doi.org/10.1093/jigpal/jzz014en
dc.referencesM. Nasieniewski, A. Pietruszczak, A method of generating modal logics defining Jaśkowski’s discussive logic D2, Studia Logica, vol. 97(1) (2011), pp. 161–182, DOI: https://doi.org/10.1007/s11225-010-9302-2en
dc.referencesM. Nasieniewski, A. Pietruszczak, On the weakest modal logics defining Jaśkowski’s logic D2 and the D2-consequence, Bulletin of the Section of Logic, vol. 41(3–4) (2012), pp. 215–232.en
dc.referencesM. Nasieniewski, A. Pietruszczak, Axiomatisations of minimal modal logics defining Jaśkowski-like discussive logics, [in:] A. Indrzejczak, J. Kaczmarek, M. Zawidzki (eds.), Trends in Logic XIII, Wydawnictwo Uniwersytetu Łódzkiego, Łódź (2014), pp. 149–163.en
dc.referencesD. Nelson, Constructible falsity, The Journal of Symbolic Logic, vol. 14 (1949), pp. 16–26, DOI: https://doi.org/10.2307/2268973en
dc.referencesH. Omori, Sette’s logics, revisited, [in:] Logic, rationality, and interaction, vol. 10455 of Lecture Notes in Computer Science, Springer, Berlin (2017), pp. 451–465, DOI: https://doi.org/10.1007/978-3-662-55665-8en
dc.referencesH. Omori, J. Alama, Axiomatizing Jaśkowski’s discussive logic ${bf D_2}$, Studia Logica, vol. 106(6) (2018), pp. 1163–1180, DOI: https://doi.org/10.1007/s11225-017-9780-6en
dc.referencesJ. Perzanowski, On M-fragments and L-fragments of normal modal propositional logics, Reports on Mathematical Logic, vol. 5 (1975), pp. 63–72.en
dc.referencesY. Petrukhin, Generalized correspondence analysis for three-valued logics, Logica Universalis, vol. 12(3-4) (2018), pp. 423–460, DOI: https://doi.org/10.1007/s11787-018-0212-9en
dc.referencesA. Pietz, U. Rivieccio, Nothing but the truth, Journal of Philosophical Logic, vol. 42(1) (2013), pp. 125–135, DOI: https://doi.org/10.1007/s10992-011-9215-1en
dc.referencesV. M. Popov, Between the logic Par and the set of all formulae, [in:] The Proceeding of the 6th Smirnov Readings in Logic, Contemporary Notebooks, Moscow (2009), pp. 93–95, (in Russian).en
dc.referencesV. M. Popov, Between Int and intuitionistic propositional logic, Logical investigations, vol. 19 (2013), pp. 197–199, URL: https://iphras.ru/uplfile/logic/log19/LI19_Popov.pdfen
dc.referencesJ. B. Rosser, Logic for mathematicians, 2nd ed., Chelsea Publishing Co., New York (1978).en
dc.referencesJ. B. Rosser, A. R. Turquette, Many-valued logics, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam (1951).en
dc.referencesA. M. Sette, On the propositional calculus P1, Mathematica Japonica, vol. 18 (1973), pp. 173–180.en
dc.referencesA. M. Sette, W. A. Carnielli, Maximal weakly-intuitionistic logics, Studia Logica, vol. 55(1) (1995), pp. 181–203, DOI: https://doi.org/10.1007/BF01053037en
dc.referencesD. J. Shoesmith, T. J. Smiley, Multiple-conclusion logic, Cambridge University Press, Cambridge-New York (1978), DOI: https://doi.org/10.1017/CBO9780511565687en
dc.referencesJ. Słupecki, G. Bryll, T. Prucnal, Some remarks on three-valued logic of J. Łukasiewicz, Studia Logica, vol. 21 (1967), pp. 45–70, DOI: https://doi.org/10.1007/BF02123418en
dc.referencesB. C. van Fraassen, Singular Terms, Truth-Value Gaps, and Free Logic, The Journal of Philosophy, vol. 63(17) (1966), pp. 481–495, URL: http://www.jstor.org/stable/2024549en
dc.referencesV. L. Vasyukov, A new axiomatization of Jaśkowski’s discussive logic, Logic and Logical Philosophy, vol. 9 (2001), pp. 35–46, DOI: https://doi.org/10.12775/llp.2001.003en
dc.referencesH. Wansing, Negation, [in:] L. Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell Philosophy Guides, Blackwell, Oxford (2001), pp. 415–436, DOI: https://doi.org/10.1002/9781405164801.ch18en
dc.contributor.authorEmailMruczek-Nasieniewska, Krystyna - mruczek@umk.pl
dc.contributor.authorEmailPetrukhin, Yaroslav - iaroslav.petrukhin@edu.uni.lodz.pl
dc.contributor.authorEmailShangin, Vasily - shangin@philos.msu.ru
dc.identifier.doi10.18778/0138-0680.2024.01
dc.relation.volume53


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