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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Detalles Bibliográficos
Publicado: 2010
Materias:
Fuzzy Kripke semantics
Gödel-Dummett logic
Many-valued modal logics
Strong completeness
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v94_n2_p189_Caicedo
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 paper:paper_00393215_v94_n2_p189_Caicedo
record_format dspace
spelling paper:paper_00393215_v94_n2_p189_Caicedo2023-06-08T15:03:30Z Standard Gödel modal logics 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. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v94_n2_p189_Caicedo 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
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.
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
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v94_n2_p189_Caicedo
http://hdl.handle.net/20.500.12110/paper_00393215_v94_n2_p189_Caicedo
_version_ 1768545178765754368

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