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Abstract:

This article deals with many-valued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones evaluated in the idempotent elements and the ones only evaluated in 0 and 1. We show how to expand an axiomatization, with canonical truth-constants in the language, of a finite residuated lattice into one of the modal logic, for each one of the three basic classes of Kripke frames. We also provide axiomatizations for the case of a finite MV chain but this time without canonical truth-constants in the language. © 2009 The Author.

Registro:

Documento: Artículo
Título:On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice
Autor:Bou, F.; Esteva, F.; Godo, L.; Rodríguez, R.O.
Filiación:Institut d'Investigació en Intel.ligncia Artificial, IIIA-CSIC, Campus UAB, Bellaterra 08193, Spain
Dpto. de Computación, Fac. Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:fuzzy logic; many-valued logic; Many-valued modal logic; modal logic; substructural logic; Computer circuits; Fuzzy logic; Lattice constants; Axiomatization; Idempotent; Kripke frames; Modal logic; Residuated lattices; Substructural logic; Many valued logics
Año:2011
Volumen:21
Número:5
Página de inicio:739
Página de fin:790
DOI: http://dx.doi.org/10.1093/logcom/exp062
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_v21_n5_p739_Bou

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Citas:

---------- APA ----------
Bou, F., Esteva, F., Godo, L. & Rodríguez, R.O. (2011) . On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice. Journal of Logic and Computation, 21(5), 739-790.
http://dx.doi.org/10.1093/logcom/exp062
---------- CHICAGO ----------
Bou, F., Esteva, F., Godo, L., Rodríguez, R.O. "On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice" . Journal of Logic and Computation 21, no. 5 (2011) : 739-790.
http://dx.doi.org/10.1093/logcom/exp062
---------- MLA ----------
Bou, F., Esteva, F., Godo, L., Rodríguez, R.O. "On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice" . Journal of Logic and Computation, vol. 21, no. 5, 2011, pp. 739-790.
http://dx.doi.org/10.1093/logcom/exp062
---------- VANCOUVER ----------
Bou, F., Esteva, F., Godo, L., Rodríguez, R.O. On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice. J Logic Comput. 2011;21(5):739-790.
http://dx.doi.org/10.1093/logcom/exp062