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  3. Formalized Mathematics
  4. Formalized Mathematics, 2022, Volume 30, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/14242
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    Pole DCWartośćJęzyk
    dc.contributor.authorInoué, Takao-
    dc.contributor.authorHanaoka, Riku-
    dc.date.accessioned2022-12-29T08:47:39Z-
    dc.date.available2022-12-29T08:47:39Z-
    dc.date.issued2022-
    dc.identifier.citationFormalized Mathematics, Volume 30, Issue 1, Pages 1-12pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/14242-
    dc.description.abstractThis paper is a continuation of Inou´e [5]. As already mentioned in the paper, a number of intuitionistic provable formulas are given with a Hilbert-style proof. For that, we make use of a family of intuitionistic deduction theorems, which are also presented in this paper by means of Mizar system [2], [1]. Our axiom system of intuitionistic propositional logic IPC is based on the propositional subsystem of H1-IQC in Troelstra and van Dalen [6, p. 68]. We also owe Heyting [4] and van Dalen [7]. Our treatment of a set-theoretic intuitionistic deduction theorem is due to Agata Darmochwał’s Mizar article “Calculus of Quantifiers. Deduction Theorem” [3].pl
    dc.language.isoenpl
    dc.publisherDeGruyter Openpl
    dc.rightsAttribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)pl
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/3.0/pl
    dc.subjectintuitionistic logicpl
    dc.subjectdeduction theorempl
    dc.subjectconsequence operatorpl
    dc.titleIntuitionistic Propositional Calculus in the Extended Framework with Modal Operator. Part IIpl
    dc.typeArticlepl
    dc.rights.holder© 2022 The Author(s)pl
    dc.rights.holderCC BY-SA 3.0 licensepl
    dc.identifier.doi10.2478/forma-2022-0001-
    dc.description.AffiliationTakao Inoué - Department of Medical Molecular Informatics, Meiji Pharmaceutical University, Tokyo, Japan; Graduate School of Science and Engineering, Hosei University, Tokyo, Japan; Department of Applied Informatics, Faculty of Science and Engineering, Hosei University, Tokyo, Japanpl
    dc.description.AffiliationRiku Hanaoka - Keyaki-Sou 403, Midori-cho 5-17-27, Koganei-city, 184-0003, Tokyo, Japanpl
    dc.description.referencesGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-817.pl
    dc.description.referencesGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.pl
    dc.description.referencesAgata Darmochwał. Calculus of quantifiers. Deduction theorem. Formalized Mathematics, 2(2):309–312, 1991.pl
    dc.description.referencesArend Heyting. Intuitionism. An introduction. Elsevier, Amsterdam, 3rd revised ed., 1971.pl
    dc.description.referencesTakao Inoué. Intuitionistic propositional calculus in the extended framework with modal operator. Part I. Formalized Mathematics, 11(3):259–266, 2003.pl
    dc.description.referencesAnne Sjerp Troelstra and Dirk van Dalen. Constructivism in mathematics. An introduction. Volume I, volume 121 of Studies in Logic and the Foundations of Mathematics. Amsterdam etc.: North-Holland, 1988. ISBN 0-444-70506-6.pl
    dc.description.referencesDirk van Dalen. Logic and Structure. London: Springer, 2013. ISBN 978-1-4471-4557-8; 978-1-4471-4558-5. doi:10.1007/978-1-4471-4558-5.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume30pl
    dc.description.issue1pl
    dc.description.firstpage1pl
    dc.description.lastpage12pl
    dc.identifier.citation2Formalized Mathematicspl
    dc.identifier.orcid0000-0002-2080-7480-
    Występuje w kolekcji(ach):Formalized Mathematics, 2022, Volume 30, Issue 1

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