Projectivity and unification in substructural logics of generalized rotations

We develop a unifying approach to study projectivity and unification in substructural logics corresponding to varieties of residuated lattices generated by generalized rotation constructions. These include many interesting varieties especially in the realm of mathematical fuzzy logics. Our main resu...

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Detalles Bibliográficos
Autores: Aglianò, Paolo, Ugolini, Sara
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/404405
Acceso en línea:http://hdl.handle.net/10261/404405
https://api.elsevier.com/content/abstract/scopus_id/85147094027
Access Level:acceso abierto
Palabra clave:Mathematical fuzzy logic
Nilpotent minimum logic
Product logic
Substructural logics
Unification
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spelling Projectivity and unification in substructural logics of generalized rotationsAglianò, PaoloUgolini, SaraMathematical fuzzy logicNilpotent minimum logicProduct logicSubstructural logicsUnificationWe develop a unifying approach to study projectivity and unification in substructural logics corresponding to varieties of residuated lattices generated by generalized rotation constructions. These include many interesting varieties especially in the realm of mathematical fuzzy logics. Our main results pertain what we shall call radical-determined varieties of rotations, which include all of the most relevant varieties in this framework. We characterize free algebras in a radical-determined variety of rotations in terms of weak Boolean products of rotations of free algebras in the variety of radicals, the latter being the intersections of maximal filters of the algebras in . Then we use such description to study projectivity in these varieties of rotations, characterizing finitely generated projective algebras. Moreover, we show that the strong unitary unification type of a variety of radicals implies the strong unitary type for the generated variety of rotations, which can be used to deduce the decidability of the admissibility of rules. As relevant applications of our general results, we obtain that product logic and nilpotent minimum logic have (strong) unitary unification type.The authors wish to thank the referees who helped improve this work. The authors declare that this work has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 890616 awarded to Ugolini.Peer reviewedElsevier BVEuropean CommissionUgolini, Sara [0000-0002-8663-042X]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202520252023info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10261/404405https://api.elsevier.com/content/abstract/scopus_id/85147094027reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/EC/H2020/890616https://doi.org/10.1016/j.ijar.2022.11.018Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/4044052026-05-22T06:33:51Z
dc.title.none.fl_str_mv Projectivity and unification in substructural logics of generalized rotations
title Projectivity and unification in substructural logics of generalized rotations
spellingShingle Projectivity and unification in substructural logics of generalized rotations
Aglianò, Paolo
Mathematical fuzzy logic
Nilpotent minimum logic
Product logic
Substructural logics
Unification
title_short Projectivity and unification in substructural logics of generalized rotations
title_full Projectivity and unification in substructural logics of generalized rotations
title_fullStr Projectivity and unification in substructural logics of generalized rotations
title_full_unstemmed Projectivity and unification in substructural logics of generalized rotations
title_sort Projectivity and unification in substructural logics of generalized rotations
dc.creator.none.fl_str_mv Aglianò, Paolo
Ugolini, Sara
author Aglianò, Paolo
author_facet Aglianò, Paolo
Ugolini, Sara
author_role author
author2 Ugolini, Sara
author2_role author
dc.contributor.none.fl_str_mv European Commission
Ugolini, Sara [0000-0002-8663-042X]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Mathematical fuzzy logic
Nilpotent minimum logic
Product logic
Substructural logics
Unification
topic Mathematical fuzzy logic
Nilpotent minimum logic
Product logic
Substructural logics
Unification
description We develop a unifying approach to study projectivity and unification in substructural logics corresponding to varieties of residuated lattices generated by generalized rotation constructions. These include many interesting varieties especially in the realm of mathematical fuzzy logics. Our main results pertain what we shall call radical-determined varieties of rotations, which include all of the most relevant varieties in this framework. We characterize free algebras in a radical-determined variety of rotations in terms of weak Boolean products of rotations of free algebras in the variety of radicals, the latter being the intersections of maximal filters of the algebras in . Then we use such description to study projectivity in these varieties of rotations, characterizing finitely generated projective algebras. Moreover, we show that the strong unitary unification type of a variety of radicals implies the strong unitary type for the generated variety of rotations, which can be used to deduce the decidability of the admissibility of rules. As relevant applications of our general results, we obtain that product logic and nilpotent minimum logic have (strong) unitary unification type.
publishDate 2023
dc.date.none.fl_str_mv 2023
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/404405
https://api.elsevier.com/content/abstract/scopus_id/85147094027
url http://hdl.handle.net/10261/404405
https://api.elsevier.com/content/abstract/scopus_id/85147094027
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/EC/H2020/890616
https://doi.org/10.1016/j.ijar.2022.11.018
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Elsevier BV
publisher.none.fl_str_mv Elsevier BV
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
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