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.
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Artículo
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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
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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
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Volumen: | 21
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Número: | 5
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Página de inicio: | 739
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Página de fin: | 790
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DOI: |
http://dx.doi.org/10.1093/logcom/exp062 |
Título revista: | Journal of Logic and Computation
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Título revista abreviado: | J Logic Comput
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ISSN: | 0955792X
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CODEN: | JLCOE
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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