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Prelinearity in (quasi-)Nelson logic

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dc.contributor.authorFlaminio, Tommaso
dc.contributor.authorRivieccio, Umberto
dc.contributor.funderprograma Horizonte 2020 (H2020) de la Comisión Europea
dc.contributor.funderMinisterio de Ciencia, Innovación y Universidades (MCIN), a través de la Agencia Estatal de Investigación (AEI), en el marco del Plan Estatal de Investigación Científica y Técnica y de Innovación
dc.date.accessioned2025-10-29T09:03:55Z
dc.date.available2025-10-29T09:03:55Z
dc.date.issued2022-09-20
dc.descriptionThe registered version of this article, first published in “Fuzzy Sets and Systems, Volume 445, 2022", is available online at the publisher's website: Elsevier, https://doi.org/10.1016/j.fss.2022.03.021
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en “Fuzzy Sets and Systems, Volume 445, 2022", está disponible en línea en el sitio web del editor: Elsevier, https://doi.org/10.1016/j.fss.2022.03.021
dc.descriptionProyecto de investigación: MOSAIC project (EU H2020-MSCA-RISE-2020 Project 101007627); Spanish project ISINC PID2019-111544GB-C21
dc.description.abstractThe algebraic theory of quasi-Nelson logic, a non-involutive generalization of Nelson's constructive logic with strong negation, has been shown to be surprisingly rich in a series of recent papers. In the present paper we bring quasi-Nelson logic into the fuzzy setting by adding the prelinearity axiom to it. We observe that the resulting system is an extension of the well-known Weak Nilpotent Minimum logic, as well as a rotation logic in the sense of recent work by P. Aglianò and S. Ugolini. We characterize the algebraic models of prelinear quasi-Nelson logic as twist-structures over Gödel algebras endowed with a nucleus operator and use the insight thus gained to look at subvarieties corresponding to extensions of well-known fuzzy systems. Our study of the quasi-Nelson negation in a prelinear setting also allows us to show that the variety of prelinear quasi-Nelson algebras is generated by a single standard algebra, thus obtaining a single chain completeness theorem for the logic.en
dc.description.versionversión final
dc.identifier.citationTommaso Flaminio, Umberto Rivieccio, Prelinearity in (quasi-)Nelson logic, Fuzzy Sets and Systems, Volume 445, 2022, Pages 66-89, ISSN 0165-0114, https://doi.org/10.1016/j.fss.2022.03.021
dc.identifier.doihttps://doi.org/10.1016/j.fss.2022.03.021
dc.identifier.issn0165-0114
dc.identifier.urihttps://hdl.handle.net/20.500.14468/30671
dc.journal.titleFuzzy Sets and Systems
dc.journal.volume445
dc.language.isoen
dc.page.final89
dc.page.initial66
dc.publisherELSEVIER
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/PID2019-111544GB-C21/ES/SISTEMAS DE INFERENCIA PARA INFORMACION INCONSISTENTE: FUNDAMENTOS LOGICOS
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/EU H2020-MSCA-RISE-2020/101007627//Modalities in Substructural Logics: Theory, Methods and Applications/MOSAIC
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.keywords(Quasi-)Nelsonen
dc.subject.keywordsWeak nilpotent minimumen
dc.subject.keywordsRotation logicsen
dc.subject.keywordsNon-involutiveen
dc.subject.keywordsPrelinear logicsen
dc.subject.keywordsAlgebraic logicen
dc.titlePrelinearity in (quasi-)Nelson logicen
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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