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2022-09-20
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info:eu-repo/semantics/openAccess
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Resumen
The 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.
Descripción
The 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
La 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
Proyecto de investigación: MOSAIC project (EU H2020-MSCA-RISE-2020 Project 101007627); Spanish project ISINC PID2019-111544GB-C21
La 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
Proyecto de investigación: MOSAIC project (EU H2020-MSCA-RISE-2020 Project 101007627); Spanish project ISINC PID2019-111544GB-C21
Categorías UNESCO
Palabras clave
(Quasi-)Nelson, Weak nilpotent minimum, Rotation logics, Non-involutive, Prelinear logics, Algebraic logic
Citación
Tommaso 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
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Facultad de Filosofía
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Lógica, Historia y Filosofía de la Ciencia