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Abstract:

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.

Registro:

Documento: Artículo
Título:Standard Gödel modal logics
Autor:Caicedo, X.; Rodriguez, R.O.
Filiación:Departamento de Matemáticas, Universidad de los Andes, A.A. 4976 Bogotá, Colombia
Departamento de Computación, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Fuzzy Kripke semantics; Gödel-Dummett logic; Many-valued modal logics; Strong completeness
Año:2010
Volumen:94
Número:2
Página de inicio:189
Página de fin:214
DOI: http://dx.doi.org/10.1007/s11225-010-9230-1
Título revista:Studia Logica
Título revista abreviado:Stud. Logica
ISSN:00393215
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v94_n2_p189_Caicedo

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Citas:

---------- APA ----------
Caicedo, X. & Rodriguez, R.O. (2010) . Standard Gödel modal logics. Studia Logica, 94(2), 189-214.
http://dx.doi.org/10.1007/s11225-010-9230-1
---------- CHICAGO ----------
Caicedo, X., Rodriguez, R.O. "Standard Gödel modal logics" . Studia Logica 94, no. 2 (2010) : 189-214.
http://dx.doi.org/10.1007/s11225-010-9230-1
---------- MLA ----------
Caicedo, X., Rodriguez, R.O. "Standard Gödel modal logics" . Studia Logica, vol. 94, no. 2, 2010, pp. 189-214.
http://dx.doi.org/10.1007/s11225-010-9230-1
---------- VANCOUVER ----------
Caicedo, X., Rodriguez, R.O. Standard Gödel modal logics. Stud. Logica. 2010;94(2):189-214.
http://dx.doi.org/10.1007/s11225-010-9230-1