Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency

In this paper, we study intermediate logics between the logic $\mathrm{G}_{\sim}^{\leq}$, the degree-preserving companion of Gödel fuzzy logic with involution $\mathrm{G}_{\sim}$, and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts $\mathrm{G...

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Detalles Bibliográficos
Autores: Coniglio, Marcelo E., Esteva Massaguer, Francesc, Gispert Brasó, Joan, Godo i Lacasa, Lluís
Tipo de recurso: capítulo de libro
Fecha de publicación:2021
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/225436
Acceso en línea:https://hdl.handle.net/2445/225436
https://doi.org/10.1007/978-3-030-71258-7_6
Access Level:acceso abierto
Palabra clave:Lògica algebraica
Lògica matemàtica
Algebraic logic
Mathematical logic
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spelling Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistencyConiglio, Marcelo E.Esteva Massaguer, FrancescGispert Brasó, JoanGodo i Lacasa, LluísLògica algebraicaLògica matemàticaAlgebraic logicMathematical logicIn this paper, we study intermediate logics between the logic $\mathrm{G}_{\sim}^{\leq}$, the degree-preserving companion of Gödel fuzzy logic with involution $\mathrm{G}_{\sim}$, and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts $\mathrm{G}_{n \sim}^{\leq}$. Although $\mathrm{G}_{\sim}^{\leq}$ and $\mathrm{G}_{n \sim}^{\leq}$are explosive w.r.t. Gödel negation $\neg$, they are paraconsistent w.r.t. the involutive negation $\sim$. We introduce the notion of saturated paraconsistency, a weaker notion than ideal paraconsistency, and we fully characterize the ideal and the saturated paraconsistent logics between $\mathrm{G}_{n \sim}^{\leq}$and CPL. We also identify a large family of saturated paraconsistent logics in the family of intermediate logics for degree-preserving finite-valued $\L$ukasiewicz logics.Springer202620262021info:eu-repo/semantics/bookPart34 p.application/pdfhttps://hdl.handle.net/2445/225436https://doi.org/10.1007/978-3-030-71258-7_6Llibres / Capítols de llibre (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésCapítol del llibre: Arieli, O., Zamansky, A. (eds) Arnon Avron on Semantics and Proof Theory of Non-Classical Logics.Outstanding Contributions to Logic, 21(c) Marcelo E. Coniglio et al., 2021info:eu-repo/semantics/openAccessoai:recercat.cat:2445/2254362026-05-29T05:05:01Z
dc.title.none.fl_str_mv Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency
title Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency
spellingShingle Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency
Coniglio, Marcelo E.
Lògica algebraica
Lògica matemàtica
Algebraic logic
Mathematical logic
title_short Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency
title_full Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency
title_fullStr Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency
title_full_unstemmed Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency
title_sort Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency
dc.creator.none.fl_str_mv Coniglio, Marcelo E.
Esteva Massaguer, Francesc
Gispert Brasó, Joan
Godo i Lacasa, Lluís
author Coniglio, Marcelo E.
author_facet Coniglio, Marcelo E.
Esteva Massaguer, Francesc
Gispert Brasó, Joan
Godo i Lacasa, Lluís
author_role author
author2 Esteva Massaguer, Francesc
Gispert Brasó, Joan
Godo i Lacasa, Lluís
author2_role author
author
author
dc.subject.none.fl_str_mv Lògica algebraica
Lògica matemàtica
Algebraic logic
Mathematical logic
topic Lògica algebraica
Lògica matemàtica
Algebraic logic
Mathematical logic
description In this paper, we study intermediate logics between the logic $\mathrm{G}_{\sim}^{\leq}$, the degree-preserving companion of Gödel fuzzy logic with involution $\mathrm{G}_{\sim}$, and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts $\mathrm{G}_{n \sim}^{\leq}$. Although $\mathrm{G}_{\sim}^{\leq}$ and $\mathrm{G}_{n \sim}^{\leq}$are explosive w.r.t. Gödel negation $\neg$, they are paraconsistent w.r.t. the involutive negation $\sim$. We introduce the notion of saturated paraconsistency, a weaker notion than ideal paraconsistency, and we fully characterize the ideal and the saturated paraconsistent logics between $\mathrm{G}_{n \sim}^{\leq}$and CPL. We also identify a large family of saturated paraconsistent logics in the family of intermediate logics for degree-preserving finite-valued $\L$ukasiewicz logics.
publishDate 2021
dc.date.none.fl_str_mv 2021
2026
2026
dc.type.none.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/225436
https://doi.org/10.1007/978-3-030-71258-7_6
url https://hdl.handle.net/2445/225436
https://doi.org/10.1007/978-3-030-71258-7_6
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Capítol del llibre: Arieli, O., Zamansky, A. (eds) Arnon Avron on Semantics and Proof Theory of Non-Classical Logics.
Outstanding Contributions to Logic, 21
dc.rights.none.fl_str_mv (c) Marcelo E. Coniglio et al., 2021
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Marcelo E. Coniglio et al., 2021
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 34 p.
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv Llibres / Capítols de llibre (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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