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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Autores principales: Caicedo, X., Rodríguez, R.O.
Formato: JOUR
Materias:
Fuzzy logic
Gödel logic
Kripke models
Many-valued logics.
Modal algebras
Modal logic
Algebra
Formal logic
Semantics
Completeness theorems
Intuitionistic modal logic
Kripke frames
Kripke model
Prelinearity
Representation theorem
Strong completeness
Many valued logics
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0955792X_v25_n1_p37_Caicedo
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0955792X_v25_n1_p37_Caicedo
record_format dspace
spelling todo:paper_0955792X_v25_n1_p37_Caicedo2023-10-03T15:51:50Z Bi-modal Gödel logic over [0,1]-valued Kripke frames Caicedo, X. Rodríguez, R.O. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Caicedo, X.
Rodríguez, R.O.
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.
format JOUR
author Caicedo, X.
Rodríguez, R.O.
author_facet Caicedo, X.
Rodríguez, R.O.
author_sort Caicedo, X.
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
url http://hdl.handle.net/20.500.12110/paper_0955792X_v25_n1_p37_Caicedo
work_keys_str_mv AT caicedox bimodalgodellogicover01valuedkripkeframes
AT rodriguezro bimodalgodellogicover01valuedkripkeframes
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