Fecha
2023-05-03
Editor/a
Director/a
Tutor/a
Coordinador/a
Prologuista
Revisor/a
Ilustrador/a
Derechos de acceso
info:eu-repo/semantics/openAccess
Título de la revista
ISSN de la revista
Título del volumen
Editorial
Taylor & Francis
Citas
0 citas en 
0 citas en 
Resumen
Quasi-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.
Descripción
The 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
La 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
Proyecto 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.
La 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
Proyecto 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.
Categorías UNESCO
Palabras clave
Nelson's constructive logic with strong negation, non-involutive, twist-structures, pocrims, subreducts
Citación
Rivieccio, 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
Centro
Facultad de Filosofía
Departamento
Lógica, Historia y Filosofía de la Ciencia