Publicación:
Compatibly involutive residuated lattices and the Nelson identity

Vista sencilla de ítem
dc.contributor.authorMatthew Spinks
dc.contributor.authorRivieccio, Umberto
dc.contributor.authorNascimento, Thiago
dc.date.accessioned2024-12-02T14:00:46Z
dc.date.available2024-12-02T14:00:46Z
dc.date.issued2018-11-03
dc.descriptionEste es el manuscrito aceptado del artículo. La versión registrada fue publicada por primera vez en Soft Comput 23, 2297–2320 (2019), está disponible en línea en el sitio web del editor: https://doi.org/10.1007/s00500-018-3588-9 This is the accepted manuscript of the article. The registered version was first published in Soft Comput 23, 2297–2320 (2019), it is available online at the publisher's website: https://doi.org/10.1007/s00500-018-3588-9
dc.description.abstractNelson’s constructive logic with strong negation N3 can be presented (to within definitional equivalence) as the axiomatic extension NInFL ew of the involutive full Lambek calculus with exchange and weakening by the Nelson axiom[Figure not available: see fulltext.] The algebraic counterpart of NInFL ew is the recently introduced class of Nelson residuated lattices. These are commutative integral bounded residuated lattices ⟨ A; ∧ , ∨ , ∗ , ⇒ , 0 , 1 ⟩ that: (i) are compatibly involutive in the sense that ∼ ∼ a= a for all a∈ A, where ∼ a: = a⇒ 0 , and (ii) satisfy the Nelson identity, namely the algebraic analogue of (Nelson ⊢ ), viz.(x⇒(x⇒y))∧(∼y⇒(∼y⇒∼x))≈x⇒y.The present paper focuses on the role played by the Nelson identity in the context of compatibly involutive commutative integral bounded residuated lattices. We present several characterisations of the identity (Nelson) in this setting, which variously permit us to comprehend its model-theoretic content from order-theoretic, syntactic, and congruence-theoretic perspectives. Notably, we show that a compatibly involutive commutative integral bounded residuated lattice A is a Nelson residuated lattice iff for all a, b∈ A, the congruence condition ΘA(0,a)=ΘA(0,b)andΘA(1,a)=ΘA(1,b)impliesa=bholds. This observation, together with others of the main results, opens the door to studying the characteristic property of Nelson residuated lattices (and hence Nelson’s constructive logic with strong negation) from a purely abstract perspective.en
dc.description.versionversión final
dc.identifier.citationSpinks, M., Rivieccio, U. & Nascimento, T. Compatibly involutive residuated lattices and the Nelson identity. Soft Comput 23, 2297–2320 (2019). https://doi.org/10.1007/s00500-018-3588-9
dc.identifier.doihttps://doi.org/10.1007/s00500-018-3588-9
dc.identifier.issn1432-7643; e-ISSN: 1433-7479
dc.identifier.urihttps://hdl.handle.net/20.500.14468/24645
dc.journal.issue7
dc.journal.titleSoft Computing
dc.journal.volume23
dc.language.isoen
dc.page.final2320
dc.page.initial2297
dc.publisherSpringer Nature
dc.relation.centerFacultades y escuelas::Facultad de Filosofía
dc.relation.departmentLógica, Historia y Filosofía de la Ciencia
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject11 Lógica
dc.subject.keywordsNelson algebraen
dc.subject.keywordsNelson logicen
dc.subject.keywordscompatibly involutive residuated latticesen
dc.subject.keywordscongruence orderableen
dc.subject.keywordsFregeanen
dc.titleCompatibly involutive residuated lattices and the Nelson identityen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
relation.isAuthorOfPublication78477d31-191f-4cbb-b9ff-32b8ec63d72b
relation.isAuthorOfPublication.latestForDiscovery78477d31-191f-4cbb-b9ff-32b8ec63d72b
Archivos
Bloque original
Mostrando 1 - 1 de 1
Miniatura
Nombre:
Rivieccio_Umberto_CompatiblyInvolutive.pdf
Tamaño:
1.05 MB
Formato:
Adobe Portable Document Format
Descargar
Bloque de licencias
Mostrando 1 - 1 de 1
No hay miniatura disponible
Nombre:
license.txt
Tamaño:
3.62 KB
Formato:
Item-specific license agreed to upon submission
Descripción:
Descargar
Colecciones
Artículos y papers