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2021-05-11
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info:eu-repo/semantics/openAccess
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Cambridge University Press
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Resumen
The variety of quasi-Nelson algebras (QNAs) has been recently introduced and characterised in several equivalent ways: among others, as (1) the class of bounded commutative integral (but non-necessarily involutive) residuated lattices satisfying the Nelson identity, as well as (2) the class of (0, 1)-congruence orderable commutative integral residuated lattices. Logically, QNAs are the algebraic counterpart of quasi-Nelson logic, which is the (algebraisable) extension of the substructural logic ℱℒew (Full Lambek calculus with Exchange and Weakening) by the Nelson axiom. In the present paper, we collect virtually all the results that are currently known on QNAs, including solutions to certain questions left open in earlier publications. Furthermore, we extend our study to some subreducts of QNAs, that is, classes of algebras corresponding to fragments of the algebraic language obtained by eliding either the implication or the lattice operations.
Descripción
The registered version of this article, first published in “Mathematical Structures in Computer Science, 31, 2021", is available online at the publisher's website: Cambridge University Press https://doi.org/10.1017/S0960129521000049
La versión registrada de este artículo, publicado por primera vez en “Mathematical Structures in Computer Science, 31, 2021", está disponible en línea en el sitio web del editor: Cambridge University Press https://doi.org/10.1017/S0960129521000049
La versión registrada de este artículo, publicado por primera vez en “Mathematical Structures in Computer Science, 31, 2021", está disponible en línea en el sitio web del editor: Cambridge University Press https://doi.org/10.1017/S0960129521000049
Categorías UNESCO
Palabras clave
(quasi-)Nelson algebras, (quasi-)Kleene algebras, weakly pseudo-complemented, twist-structures
Citación
Ramon Jansana, Umberto Rivieccio, Quasi-Nelson algebras and fragments. Mathematical Structures in Computer Science, 31, 2021, pp. 257–285. Preprint. doi: 10.1017/S0960129521000049
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Facultad de Filosofía
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Lógica, Historia y Filosofía de la Ciencia