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Fragments of Quasi-Nelson: The Algebraizable Core

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dc.contributor.authorRivieccio, Umberto
dc.contributor.funderCNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brasil
dc.date.accessioned2025-10-29T07:58:18Z
dc.date.available2025-10-29T07:58:18Z
dc.date.issued2022-10-01
dc.descriptionThe registered version of this article, first published in “Logic Journal of the IGPL, Volume 30, 2022", is available online at the publisher's website: Oxford University Press, https://doi.org/10.1093/jigpal/jzab023
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en “Logic Journal of the IGPL, Volume 30, 2022", está disponible en línea en el sitio web del editor: Oxford University Press, https://doi.org/10.1093/jigpal/jzab023
dc.descriptionFinanciado por: Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil), under the grant 313643/2017-2
dc.description.abstractThis is the second of a series of papers that investigate fragments of quasi-Nelson logic (QNL) from an algebraic logic standpoint. QNL, recently introduced as a common generalization of intuitionistic and Nelson’s constructive logic with strong negation, is the axiomatic extension of the substructural logic (full Lambek calculus with exchange and weakening) by the Nelson axiom. The algebraic counterpart of QNL (quasi-Nelson algebras) is a class of commutative integral residuated lattices (a.k.a. -algebras) that includes both Heyting and Nelson algebras and can be characterized algebraically in several alternative ways. The present paper focuses on the algebraic counterpart (a class we dub quasi-Nelson implication algebras, QNI-algebras) of the implication–negation fragment of QNL, corresponding to the connectives that witness the algebraizability of QNL. We recall the main known results on QNI-algebras and establish a number of new ones. Among these, we show that QNI-algebras form a congruence-distributive variety (Cor. 3.15) that enjoys equationally definable principal congruences and the strong congruence extension property (Prop. 3.16); we also characterize the subdirectly irreducible QNI-algebras in terms of the underlying poset structure (Thm. 4.23). Most of these results are obtained thanks to twist representations for QNI-algebras, which generalize the known ones for Nelson and quasi-Nelson algebras; we further introduce a Hilbert-style calculus that is algebraizable and has the variety of QNI-algebras as its equivalent algebraic semantics.en
dc.description.versionversión original
dc.identifier.citationUmberto Rivieccio, Fragments of Quasi-Nelson: The Algebraizable Core, Logic Journal of the IGPL, Volume 30, Issue 5, October 2022, Pages 807–839, https://doi.org/10.1093/jigpal/jzab023
dc.identifier.doihttps://doi.org/10.1093/jigpal/jzab023
dc.identifier.issn1367-0751 | eISSN 1368-9894
dc.identifier.urihttps://hdl.handle.net/20.500.14468/30670
dc.journal.issue5
dc.journal.titleLogic Journal of the IGPL
dc.journal.volume30
dc.language.isoen
dc.page.final839
dc.page.initial807
dc.publisherOxford University Press
dc.relation.centerFacultad de Filosofía
dc.relation.departmentLógica, Historia y Filosofía de la Ciencia
dc.relation.projectidinfo:eu-repo/grantAgreement/CNPq/313643/2017-2
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject72 Filosofía
dc.subject11 Lógica
dc.titleFragments of Quasi-Nelson: The Algebraizable Coreen
dc.typeartículoes
dc.typejournal articleen
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relation.isAuthorOfPublication.latestForDiscovery78477d31-191f-4cbb-b9ff-32b8ec63d72b
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