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Abstract:

Using the theory of BL-algebras, it is shown that a prepositional formula φ is derivable in Łukasiewicz infinite valued Logic if and only if its double negation ∼∼ φ is derivable in Hájek Basic Fuzzy logic. If SBL is the extension of Basic Logic by the axiom (φ & (φ ⇒ ∼ φ)) ⇒ ψ, then φ is derivable in in classical logic if and only if ∼∼ φ is derivable in SBL. Axiomatic extensions of Basic Logic are in correspondence with subvarieties of the variety of BL-algebras. It is shown that the MV-algebra of regular elements of a free algebra in a subvariety of BL-algebras is free in the corresponding subvariety of MV-algebras, with the same number of free generators. Similar results are obtained for the generalized BL-algebras of dense elements of free BL-algebras.

Registro:

Documento: Artículo
Título:Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic
Autor:Cignoli, R.; Torrens, A.
Filiación:Departamento de Matemática, Fac. Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
Palabras clave:Łukasiewicz logic; Basic fuzzy logic; BL-algebras; Glivenko's theorem; MV-algebras
Año:2003
Volumen:42
Número:4
Página de inicio:361
Página de fin:370
DOI: http://dx.doi.org/10.1007/s001530200144
Título revista:Archive for Mathematical Logic
Título revista abreviado:Arch. Math. Logic
ISSN:09335846
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09335846_v42_n4_p361_Cignoli

Referencias:

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Citas:

---------- APA ----------
Cignoli, R. & Torrens, A. (2003) . Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic. Archive for Mathematical Logic, 42(4), 361-370.
http://dx.doi.org/10.1007/s001530200144
---------- CHICAGO ----------
Cignoli, R., Torrens, A. "Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic" . Archive for Mathematical Logic 42, no. 4 (2003) : 361-370.
http://dx.doi.org/10.1007/s001530200144
---------- MLA ----------
Cignoli, R., Torrens, A. "Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic" . Archive for Mathematical Logic, vol. 42, no. 4, 2003, pp. 361-370.
http://dx.doi.org/10.1007/s001530200144
---------- VANCOUVER ----------
Cignoli, R., Torrens, A. Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic. Arch. Math. Logic. 2003;42(4):361-370.
http://dx.doi.org/10.1007/s001530200144