REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU
UwB

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dc.contributor.authorSawicki, Damian-
dc.contributor.authorGrabowski, Adam-
dc.date.accessioned2022-01-03T13:33:16Z-
dc.date.available2022-01-03T13:33:16Z-
dc.date.issued2021-
dc.identifier.citationFormalized Mathematics, Volume 29, Issue 2, Pages 77-85pl
dc.identifier.issn1426-2630-
dc.identifier.urihttp://hdl.handle.net/11320/12387-
dc.description.abstractThe main aim of this article is to introduce formally two generalizations of lattices, namely weakly associative lattices and near lattices, which can be obtained from the former by certain weakening of the usual well-known axioms. We show selected propositions devoted to weakly associative lattices and near lattices from Chapter 6 of [15], dealing also with alternative versions of classical axiomatizations. Some of the results were proven in the Mizar [1], [2] system with the help of Prover9 [14] proof assistant.pl
dc.language.isoenpl
dc.publisherDeGruyter Openpl
dc.rightsAttribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)-
dc.rights.urihttps://creativecommons.org/licenses/by-sa/3.0/-
dc.subjectweakly associative latticepl
dc.subjectnear latticepl
dc.titleOn Weakly Associative Lattices and Near Latticespl
dc.typeArticlepl
dc.rights.holder© 2021 University of Białymstokupl
dc.rights.holderCC-BY-SA License ver. 3.0 or laterpl
dc.identifier.doi10.2478/forma-2021-0008-
dc.description.AffiliationDamian Sawicki - Institute of Informatics, University of Białystok, Polandpl
dc.description.AffiliationAdam Grabowski - Institute of Informatics, University of Białystok, Polandpl
dc.description.referencesGrzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, 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:10.1007/978-3-319-20615-8_17.pl
dc.description.referencesGrzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pak. 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
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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 Damian Sawicki. On two alternative axiomatizations of lattices by McKenzie and Sholander. Formalized Mathematics, 26(2):193–198, 2018. doi:10.2478/forma-2018-0017.pl
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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
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dc.description.referencesDominik Kulesza and Adam Grabowski. Formalization of quasilattices. Formalized Mathematics, 28(2):217–225, 2020. doi:10.2478/forma-2020-0019.pl
dc.description.referencesWilliam McCune. Prover9 and Mace4. 2005–2010.pl
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dc.identifier.eissn1898-9934-
dc.description.volume29pl
dc.description.issue2pl
dc.description.firstpage77pl
dc.description.lastpage85pl
dc.identifier.citation2Formalized Mathematicspl
dc.identifier.orcidbrakorcid-
dc.identifier.orcid0000-0001-5026-3990-
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Formalized Mathematics, 2021, Volume 29, Issue 2

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