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Fragments of quasi-Nelson: residuation

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dc.contributor.authorRivieccio, Umberto
dc.contributor.funderMinistry of Science and Innovation of Spain
dc.date.accessioned2025-10-29T10:29:52Z
dc.date.available2025-10-29T10:29:52Z
dc.date.issued2023-05-03
dc.descriptionThe registered version of this article, first published in “Journal of Applied Non-Classical Logics, 33, 2023", is available online at the publisher's website: Taylor &Francis, https://doi.org/10.1080/11663081.2023.2203312
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en “Journal of Applied Non-Classical Logics, 33, 2023", está disponible en línea en el sitio web del editor: Taylor &Francis, https://doi.org/10.1080/11663081.2023.2203312
dc.descriptionProyecto de investigación: I+D+i research project [grant number PID2019-110843GA-I00] La geometría de las lógicas no-clásicas funded by the Ministry of Science and Innovation of Spain.
dc.description.abstractQuasi-Nelson logic (QNL) was recently introduced as a common generalisation of intuitionistic logic and Nelson's constructive logic with strong negation. Viewed as a substructural logic, QNL is the axiomatic extension of the Full Lambek Calculus with Exchange and Weakening by the Nelson axiom, and its algebraic counterpart is a variety of residuated lattices called quasi-Nelson algebras. Nelson's logic, in turn, may be obtained as the axiomatic extension of QNL by the double negation (or involutivity) axiom, and intuitionistic logic as the extension of QNL by the contraction axiom. A recent series of papers by the author and collaborators initiated the study of fragments of QNL, which correspond to subreducts of quasi-Nelson algebras. In the present paper we focus on fragments that contain the connectives forming a residuated pair (the monoid conjunction and the so-called strong Nelson implication), these being the most interesting ones from a substructural logic perspective. We provide quasi-equational (whenever possible, equational) axiomatisations for the corresponding classes of algebras, obtain twist representations for them, study their congruence properties and take a look at a few notable subvarieties. Our results specialise to the involutive case, yielding characterisations of the corresponding fragments of Nelson's logic and their algebraic counterparts.en
dc.description.versionversión final
dc.identifier.citationRivieccio, U. (2023). Fragments of quasi-Nelson: residuation. Journal of Applied Non-Classical Logics, 33(1), 52–119. https://doi.org/10.1080/11663081.2023.2203312
dc.identifier.doihttps://doi.org/10.1080/11663081.2023.2203312
dc.identifier.issn1166-3081 | eISSN 1958-5780
dc.identifier.urihttps://hdl.handle.net/20.500.14468/30676
dc.journal.issue1
dc.journal.titleJournal of Applied Non-Classical Logics
dc.journal.volume33
dc.language.isoen
dc.page.final119
dc.page.initial52
dc.publisherTaylor & Francis
dc.relation.centerFacultad de Filosofía
dc.relation.departmentLógica, Historia y Filosofía de la Ciencia
dc.relation.projectidinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019- 110843GA-I00/ES/LA GEOMETRIA DE LAS LOGICAS NO-CLASICAS
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.subject.keywordsNelson's constructive logic with strong negationen
dc.subject.keywordsnon-involutiveen
dc.subject.keywordstwist-structuresen
dc.subject.keywordspocrimsen
dc.subject.keywordssubreductsen
dc.titleFragments of quasi-Nelson: residuationen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
relation.isAuthorOfPublication78477d31-191f-4cbb-b9ff-32b8ec63d72b
relation.isAuthorOfPublication.latestForDiscovery78477d31-191f-4cbb-b9ff-32b8ec63d72b
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