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  3. Formalized Mathematics
  4. Formalized Mathematics, 2024, Volume 32, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/17802
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    Pole DCWartośćJęzyk
    dc.contributor.authorGrabowski, Adam-
    dc.contributor.authorTurowski, Franciszek-
    dc.date.accessioned2025-01-10T10:59:37Z-
    dc.date.available2025-01-10T10:59:37Z-
    dc.date.issued2024-
    dc.identifier.citationFormalized Mathematics, Volume 32, Issue 1, Pages 271–279pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/17802-
    dc.description.abstractThe main aim of this article is to construct two non-trivial examples of weakly associative lattices (also known as trellises). These are generalizations of lattices, not assuming associativity of the lattice operations. We show some connections between trellises and tolerance relations according to the paper of Chajda and Zelinka.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.subjecttrellispl
    dc.subjecttolerancepl
    dc.subjectweakly associative latticepl
    dc.titleFormalization of Trellises and Tolerance Relationspl
    dc.typeArticlepl
    dc.rights.holder© 2024 The Author(s)pl
    dc.rights.holderCC BY-SA 3.0 licensepl
    dc.identifier.doi10.2478/forma-2024-0022-
    dc.description.AffiliationAdam Grabowski - Faculty of Computer Science, University of Białystok, Polandpl
    dc.description.AffiliationFranciszek Turowski - Faculty of Computer Science, University of Białystok, Polandpl
    dc.description.referencesGarrett Birkhoff. Lattice Theory. Providence, Rhode Island, New York, 1967.pl
    dc.description.referencesIvan Chajda and Bohdan Zelinka. Weakly associative lattices and tolerance relations. Czechoslovak Mathematical Journal, 26(2):259–269, 1976.pl
    dc.description.referencesB.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 2002.pl
    dc.description.referencesErvin Fried and George Grätzer. Some examples of weakly associative lattices. Colloquium Mathematicum, 27:215–221, 1973. doi:10.4064/cm-27-2-215-221.pl
    dc.description.referencesAdam Grabowski. On fuzzy negations and laws of contraposition. Lattice of fuzzy nega tions. Formalized Mathematics, 31(1):151–159, 2023. doi:10.2478/forma-2023-0014.pl
    dc.description.referencesAdam Grabowski. Mechanizing complemented lattices within Mizar system. Journal of Automated Reasoning, 55:211–221, 2015. doi:10.1007/s10817-015-9333-5.pl
    dc.description.referencesAdam Grabowski. Lattice theory for rough sets – a case study with Mizar. Fundamenta Informaticae, 147(2–3):223–240, 2016. doi:10.3233/FI-2016-1406.pl
    dc.description.referencesAdam Grabowski and Takashi Mitsuishi. Extending Formal Fuzzy Sets with Triangular Norms and Conorms, volume 642: Advances in Intelligent Systems and Computing, pages 176–187. Springer International Publishing, Cham, 2018. doi:10.1007/978-3-319-66824-6_16.pl
    dc.description.referencesAdam Grabowski and Takashi Mitsuishi. Formalizing lattice-theoretical aspects of rough and fuzzy sets. In D. Ciucci, G. Wang, S. Mitra, and W.Z. Wu, editors, Rough Sets and Knowledge Technology – 10th International Conference held as part of the International Joint Conference on Rough Sets (IJCRS), Tianjin, PR China, November 20–23, 2015, Proceedings, volume 9436 of Lecture Notes in Artificial Intelligence, pages 347–356. Springer, 2015. doi:10.1007/978-3-319-25754-9_31.pl
    dc.description.referencesAdam Grabowski and Markus Moschner. Managing heterogeneous theories within a mathematical knowledge repository. In Andrea Asperti, Grzegorz Bancerek, and Andrzej Trybulec, editors, Mathematical Knowledge Management Proceedings, volume 3119 of Lecture Notes in Computer Science, pages 116–129. Springer, 2004. doi:10.1007/978-3-540-27818-4 9. 3rd International Conference on Mathematical Knowledge Management, Bialowieza, Poland, Sep. 19–21, 2004.pl
    dc.description.referencesAdam Grabowski and Christoph Schwarzweller. Translating mathematical vernacular into knowledge repositories. In Michael Kohlhase, editor, Mathematical Knowledge Management, volume 3863 of Lecture Notes in Computer Science, pages 49–64. Springer, 2006. doi:10.1007/11618027 4. 4th International Conference on Mathematical Knowledge Management, Bremen, Germany, MKM 2005, July 15–17, 2005, Revised Selected Papers.pl
    dc.description.referencesAdam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. Equality in computer proof-assistants. In Ganzha, Maria and Maciaszek, Leszek and Paprzycki, Marcin, editor, Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, volume 5 of ACSIS-Annals of Computer Science and Information Systems, pages 45–54. IEEE, 2015. doi:10.15439/2015F229.pl
    dc.description.referencesGeorge Grätzer. General Lattice Theory. Academic Press, New York, 1978.pl
    dc.description.referencesGeorge Grätzer. Lattice Theory: Foundation. Birkh¨auser, 2011.pl
    dc.description.referencesYu Kong and Bin Zhao. Uninorms on bounded trellises. Fuzzy Sets and Systems, 481: 108898, 2024. doi:10.1016/j.fss.2024.108898.pl
    dc.description.referencesWilliam McCune and Ranganathan Padmanabhan. Automated Deduction in Equational Logic and Cubic Curves. Springer-Verlag, Berlin, 1996.pl
    dc.description.referencesRanganathan Padmanabhan and Sergiu Rudeanu. Axioms for Lattices and Boolean Algebras. World Scientific Publishers, 2008.pl
    dc.description.referencesDamian Sawicki and Adam Grabowski. On weakly associative lattices and near lattices. Formalized Mathematics, 29(2):77–85, 2021. doi:10.2478/forma-2021-0008.pl
    dc.description.referencesHelen Skala. Trellis Theory. Providence, R.I.: American Mathematical Society, 1972.pl
    dc.description.referencesHelen L. Skala. Trellis theory. Algebra Universalis, 1:218–233, 1971. doi:10.1007/BF02944982.pl
    dc.description.referencesLemnaouar Zedam and Bernard De Baets. Triangular norms on bounded trellises. Fuzzy Sets and Systems, 462:108468, 2023. doi:10.1016/j.fss.2023.01.003.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume32pl
    dc.description.issue1pl
    dc.description.firstpage271pl
    dc.description.lastpage279pl
    dc.identifier.citation2Formalized Mathematicspl
    dc.identifier.orcid0000-0001-5026-3990-
    Występuje w kolekcji(ach):Formalized Mathematics, 2024, Volume 32, Issue 1

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