Fragments of quasi-Nelson: residuation

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,...

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Detalles Bibliográficos
Autor: Rivieccio, Umberto
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/30676
Acceso en línea:https://hdl.handle.net/20.500.14468/30676
Access Level:acceso abierto
Palabra clave:72 Filosofía
11 Lógica
Nelson's constructive logic with strong negation
non-involutive
twist-structures
pocrims
subreducts
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oai_identifier_str oai:e-spacio.uned.es:20.500.14468/30676
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spelling Fragments of quasi-Nelson: residuationRivieccio, Umberto72 Filosofía11 LógicaNelson's constructive logic with strong negationnon-involutivetwist-structurespocrimssubreductsQuasi-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.Taylor & FrancisMinistry of Science and Innovation of Spaine-Spacio UNED20252025-10-2920232023-05-0320232023-05-03journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14468/30676reponame:e-spacio. Repositorio Institucional de la UNEDinstname:Universidad Nacional de Educación a DistanciaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.esoai:e-spacio.uned.es:20.500.14468/306762026-06-06T12:38:31Z
dc.title.none.fl_str_mv Fragments of quasi-Nelson: residuation
title Fragments of quasi-Nelson: residuation
spellingShingle Fragments of quasi-Nelson: residuation
Rivieccio, Umberto
72 Filosofía
11 Lógica
Nelson's constructive logic with strong negation
non-involutive
twist-structures
pocrims
subreducts
title_short Fragments of quasi-Nelson: residuation
title_full Fragments of quasi-Nelson: residuation
title_fullStr Fragments of quasi-Nelson: residuation
title_full_unstemmed Fragments of quasi-Nelson: residuation
title_sort Fragments of quasi-Nelson: residuation
dc.creator.none.fl_str_mv Rivieccio, Umberto
author Rivieccio, Umberto
author_facet Rivieccio, Umberto
author_role author
dc.contributor.none.fl_str_mv Ministry of Science and Innovation of Spain
e-Spacio UNED
dc.subject.none.fl_str_mv 72 Filosofía
11 Lógica
Nelson's constructive logic with strong negation
non-involutive
twist-structures
pocrims
subreducts
topic 72 Filosofía
11 Lógica
Nelson's constructive logic with strong negation
non-involutive
twist-structures
pocrims
subreducts
description 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.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-05-03
2023
2023-05-03
2025
2025-10-29
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14468/30676
url https://hdl.handle.net/20.500.14468/30676
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:e-spacio. Repositorio Institucional de la UNED
instname:Universidad Nacional de Educación a Distancia
instname_str Universidad Nacional de Educación a Distancia
reponame_str e-spacio. Repositorio Institucional de la UNED
collection e-spacio. Repositorio Institucional de la UNED
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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