Standard Gödel modal logics

We prove strong completeness of the □-version and the {lozenge, open}-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both infinitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the f...

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Autores principales: Caicedo, X., Rodriguez, R.O.
Formato: JOUR
Materias:
Fuzzy Kripke semantics
Gödel-Dummett logic
Many-valued modal logics
Strong completeness
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00393215_v94_n2_p189_Caicedo
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00393215_v94_n2_p189_Caicedo
record_format dspace
spelling todo:paper_00393215_v94_n2_p189_Caicedo2023-10-03T14:49:42Z Standard Gödel modal logics Caicedo, X. Rodriguez, R.O. Fuzzy Kripke semantics Gödel-Dummett logic Many-valued modal logics Strong completeness We prove strong completeness of the □-version and the {lozenge, open}-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both infinitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the first logic is reducible to the class of frames having two-valued accessibility relation and this logic does not enjoy the finite model property, while validity in the second logic requires truly fuzzy accessibility relations and this logic has the finite model property. Analogues of the classical modal systems D, T, S4 and S5 are considered also, and the completeness results are extended to languages enriched with a discrete well ordered set of truth constants. © 2010 Springer Science+Business Media B.V. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00393215_v94_n2_p189_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 Kripke semantics
Gödel-Dummett logic
Many-valued modal logics
Strong completeness
spellingShingle Fuzzy Kripke semantics
Gödel-Dummett logic
Many-valued modal logics
Strong completeness
Caicedo, X.
Rodriguez, R.O.
Standard Gödel modal logics
topic_facet Fuzzy Kripke semantics
Gödel-Dummett logic
Many-valued modal logics
Strong completeness
description We prove strong completeness of the □-version and the {lozenge, open}-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both infinitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the first logic is reducible to the class of frames having two-valued accessibility relation and this logic does not enjoy the finite model property, while validity in the second logic requires truly fuzzy accessibility relations and this logic has the finite model property. Analogues of the classical modal systems D, T, S4 and S5 are considered also, and the completeness results are extended to languages enriched with a discrete well ordered set of truth constants. © 2010 Springer Science+Business Media B.V.
format JOUR
author Caicedo, X.
Rodriguez, R.O.
author_facet Caicedo, X.
Rodriguez, R.O.
author_sort Caicedo, X.
title Standard Gödel modal logics
title_short Standard Gödel modal logics
title_full Standard Gödel modal logics
title_fullStr Standard Gödel modal logics
title_full_unstemmed Standard Gödel modal logics
title_sort standard gödel modal logics
url http://hdl.handle.net/20.500.12110/paper_00393215_v94_n2_p189_Caicedo
work_keys_str_mv AT caicedox standardgodelmodallogics
AT rodriguezro standardgodelmodallogics
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