Bi-modal Gödel logic over [0,1]-valued Kripke frames
We consider the Gödel bi-modal logic determined by fuzzy Kripke models where both the propositions and the accessibility relation are infinitely valued over the standard Gödel algebra [0,1], and prove strong completeness of the Fischer Servi intuitionistic modal logic IK plus the prelinearity axiom...
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Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0955792X_v25_n1_p37_Caicedo http://hdl.handle.net/20.500.12110/paper_0955792X_v25_n1_p37_Caicedo |
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paper:paper_0955792X_v25_n1_p37_Caicedo2023-06-08T15:55:56Z Bi-modal Gödel logic over [0,1]-valued Kripke frames Fuzzy logic Gödel logic Kripke models Many-valued logics. Modal algebras Modal logic Algebra Formal logic Fuzzy logic Semantics Completeness theorems Intuitionistic modal logic Kripke frames Kripke model Modal logic Prelinearity Representation theorem Strong completeness Many valued logics We consider the Gödel bi-modal logic determined by fuzzy Kripke models where both the propositions and the accessibility relation are infinitely valued over the standard Gödel algebra [0,1], and prove strong completeness of the Fischer Servi intuitionistic modal logic IK plus the prelinearity axiom with respect to this semantics. We axiomatize also the bi-modal analogues of classical T, S4 and S5, obtained by restricting to models over frames satisfying the [0,1]-valued versions of the structural properties which characterize these logics. As an application of the completeness theorems we obtain a representation theorem for bi-modal Gödel algebras. © 2012 © The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0955792X_v25_n1_p37_Caicedo http://hdl.handle.net/20.500.12110/paper_0955792X_v25_n1_p37_Caicedo |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
Fuzzy logic Gödel logic Kripke models Many-valued logics. Modal algebras Modal logic Algebra Formal logic Fuzzy logic Semantics Completeness theorems Intuitionistic modal logic Kripke frames Kripke model Modal logic Prelinearity Representation theorem Strong completeness Many valued logics |
spellingShingle |
Fuzzy logic Gödel logic Kripke models Many-valued logics. Modal algebras Modal logic Algebra Formal logic Fuzzy logic Semantics Completeness theorems Intuitionistic modal logic Kripke frames Kripke model Modal logic Prelinearity Representation theorem Strong completeness Many valued logics Bi-modal Gödel logic over [0,1]-valued Kripke frames |
topic_facet |
Fuzzy logic Gödel logic Kripke models Many-valued logics. Modal algebras Modal logic Algebra Formal logic Fuzzy logic Semantics Completeness theorems Intuitionistic modal logic Kripke frames Kripke model Modal logic Prelinearity Representation theorem Strong completeness Many valued logics |
description |
We consider the Gödel bi-modal logic determined by fuzzy Kripke models where both the propositions and the accessibility relation are infinitely valued over the standard Gödel algebra [0,1], and prove strong completeness of the Fischer Servi intuitionistic modal logic IK plus the prelinearity axiom with respect to this semantics. We axiomatize also the bi-modal analogues of classical T, S4 and S5, obtained by restricting to models over frames satisfying the [0,1]-valued versions of the structural properties which characterize these logics. As an application of the completeness theorems we obtain a representation theorem for bi-modal Gödel algebras. © 2012 © The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com. |
title |
Bi-modal Gödel logic over [0,1]-valued Kripke frames |
title_short |
Bi-modal Gödel logic over [0,1]-valued Kripke frames |
title_full |
Bi-modal Gödel logic over [0,1]-valued Kripke frames |
title_fullStr |
Bi-modal Gödel logic over [0,1]-valued Kripke frames |
title_full_unstemmed |
Bi-modal Gödel logic over [0,1]-valued Kripke frames |
title_sort |
bi-modal gödel logic over [0,1]-valued kripke frames |
publishDate |
2015 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0955792X_v25_n1_p37_Caicedo http://hdl.handle.net/20.500.12110/paper_0955792X_v25_n1_p37_Caicedo |
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1768545151697813504 |