Flaminio, TommasoRivieccio, Umberto2025-10-292025-10-292022-09-20Tommaso 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.2022.03.0210165-0114https://doi.org/10.1016/j.fss.2022.03.021https://hdl.handle.net/20.500.14468/30671The 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.2022.03.021La 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.2022.03.021Proyecto de investigación: MOSAIC project (EU H2020-MSCA-RISE-2020 Project 101007627); Spanish project ISINC PID2019-111544GB-C21The 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.eninfo:eu-repo/semantics/openAccess72 Filosofía11 Lógicaartículo(Quasi-)NelsonWeak nilpotent minimumRotation logicsNon-involutivePrelinear logicsAlgebraic logic