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Abstract:

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.

Registro:

Documento: Artículo
Título:Bi-modal Gödel logic over [0,1]-valued Kripke frames
Autor:Caicedo, X.; Rodríguez, R.O.
Filiación:Departamento de Matemáticas, Universidad de Los Andes, Bogotá, Colombia
Departamento de Computación, Fac. Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Palabras clave: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
Año:2015
Volumen:25
Número:1
Página de inicio:37
Página de fin:55
DOI: http://dx.doi.org/10.1093/logcom/exs036
Título revista:Journal of Logic and Computation
Título revista abreviado:J Logic Comput
ISSN:0955792X
CODEN:JLCOE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0955792X_v25_n1_p37_Caicedo

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Citas:

---------- APA ----------
Caicedo, X. & Rodríguez, R.O. (2015) . Bi-modal Gödel logic over [0,1]-valued Kripke frames. Journal of Logic and Computation, 25(1), 37-55.
http://dx.doi.org/10.1093/logcom/exs036
---------- CHICAGO ----------
Caicedo, X., Rodríguez, R.O. "Bi-modal Gödel logic over [0,1]-valued Kripke frames" . Journal of Logic and Computation 25, no. 1 (2015) : 37-55.
http://dx.doi.org/10.1093/logcom/exs036
---------- MLA ----------
Caicedo, X., Rodríguez, R.O. "Bi-modal Gödel logic over [0,1]-valued Kripke frames" . Journal of Logic and Computation, vol. 25, no. 1, 2015, pp. 37-55.
http://dx.doi.org/10.1093/logcom/exs036
---------- VANCOUVER ----------
Caicedo, X., Rodríguez, R.O. Bi-modal Gödel logic over [0,1]-valued Kripke frames. J Logic Comput. 2015;25(1):37-55.
http://dx.doi.org/10.1093/logcom/exs036