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Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-29870
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dc.contributor.authorKwuida, Léonard-
dc.contributor.authorMachida, Hajime-
dc.date.accessioned2024-02-08T14:53:20Z-
dc.date.available2024-02-08T14:53:20Z-
dc.date.issued2010-
dc.identifier.issn1012-2443de_CH
dc.identifier.issn1573-7470de_CH
dc.identifier.urihttps://digitalcollection.zhaw.ch/handle/11475/29870-
dc.descriptionErworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)de_CH
dc.description.abstractWeakly dicomplemented lattices are bounded lattices equipped with two unary operations to encode a negation on concepts. They have been introduced to capture the equational theory of concept algebras (Wille 2000; Kwuida 2004). They generalize Boolean algebras. Concept algebras are concept lattices, thus complete lattices, with a weak negation and a weak opposition. A special case of the representation problem for weakly dicomplemented lattices, posed in Kwuida (2004), is whether complete weakly dicomplemented lattices are isomorphic to concept algebras. In this contribution we give a negative answer to this question (Theorem 4). We also provide a new proof of a well known result due to M.H. Stone (Trans Am Math Soc 40:37–111, 1936), saying that each Boolean algebra is a field of sets (Corollary 4). Before these, we prove that the boundedness condition on the initial definition of weakly dicomplemented lattices (Definition 1) is superfluous (Theorem 1, see also Kwuida (2009)).de_CH
dc.language.isoende_CH
dc.publisherSpringerde_CH
dc.relation.ispartofAnnals of Mathematics and Artificial Intelligencede_CH
dc.rightsLicence according to publishing contractde_CH
dc.subjectConcept algebrasde_CH
dc.subjectNegationde_CH
dc.subjectWeakly dicomplemented latticesde_CH
dc.subjectRepresentation problemde_CH
dc.subjectBoolean algebrasde_CH
dc.subjectField of setsde_CH
dc.subjectFormal concept analysisde_CH
dc.subject.ddc510: Mathematikde_CH
dc.titleOn the isomorphism problem of concept algebrasde_CH
dc.typeBeitrag in wissenschaftlicher Zeitschriftde_CH
dcterms.typeTextde_CH
zhaw.departementSchool of Engineeringde_CH
zhaw.organisationalunitInstitut für Angewandte Mathematik und Physik (IAMP)de_CH
dc.identifier.doi10.1007/s10472-010-9194-xde_CH
dc.identifier.doi10.21256/zhaw-29870-
zhaw.funding.euNode_CH
zhaw.issue2de_CH
zhaw.originated.zhawYesde_CH
zhaw.pages.end239de_CH
zhaw.pages.start223de_CH
zhaw.publication.statuspublishedVersionde_CH
zhaw.volume59de_CH
zhaw.publication.reviewPeer review (Publikation)de_CH
zhaw.author.additionalNode_CH
zhaw.display.portraitYesde_CH
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Kwuida, L., & Machida, H. (2010). On the isomorphism problem of concept algebras. Annals of Mathematics and Artificial Intelligence, 59(2), 223–239. https://doi.org/10.1007/s10472-010-9194-x
Kwuida, L. and Machida, H. (2010) ‘On the isomorphism problem of concept algebras’, Annals of Mathematics and Artificial Intelligence, 59(2), pp. 223–239. Available at: https://doi.org/10.1007/s10472-010-9194-x.
L. Kwuida and H. Machida, “On the isomorphism problem of concept algebras,” Annals of Mathematics and Artificial Intelligence, vol. 59, no. 2, pp. 223–239, 2010, doi: 10.1007/s10472-010-9194-x.
KWUIDA, Léonard und Hajime MACHIDA, 2010. On the isomorphism problem of concept algebras. Annals of Mathematics and Artificial Intelligence. 2010. Bd. 59, Nr. 2, S. 223–239. DOI 10.1007/s10472-010-9194-x
Kwuida, Léonard, and Hajime Machida. 2010. “On the Isomorphism Problem of Concept Algebras.” Annals of Mathematics and Artificial Intelligence 59 (2): 223–39. https://doi.org/10.1007/s10472-010-9194-x.
Kwuida, Léonard, and Hajime Machida. “On the Isomorphism Problem of Concept Algebras.” Annals of Mathematics and Artificial Intelligence, vol. 59, no. 2, 2010, pp. 223–39, https://doi.org/10.1007/s10472-010-9194-x.


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