Abstract:
The classical Glivenko theorem asserts that a prepositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK-logic with negation we understand an algebraizable logic whose language is an expansion of the language of BCK-logic with negation by a family of connectives implicitly defined by equations and compatible with BCK-congruences. Many of the logics in the current literature are natural expansions of BCK-logic with negation. The validity of the analogous of Glivenko theorem in these logics is equivalent to the validity of a simple one-variable formula in the language of BCK-logic with negation. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Registro:
Documento: |
Artículo
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Título: | Glivenko like theorems in natural expansions of BCK-logic |
Autor: | Cignoli, R.; Torrell, A.T. |
Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
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Palabras clave: | Algebraic semantics; Bounded BCK-algebra; Bounded BCK-logic; Bounded pocrim; Glivenko's theorem; Involutive BCK-algebra; Natural expansion of a logic; Natural expansion of a quasivariety; Regular element |
Año: | 2004
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Volumen: | 50
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Número: | 2
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Página de inicio: | 111
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Página de fin: | 125
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DOI: |
http://dx.doi.org/10.1002/malq.200310082 |
Título revista: | Mathematical Logic Quarterly
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Título revista abreviado: | Math. Logic Q.
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ISSN: | 09425616
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09425616_v50_n2_p111_Cignoli |
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Citas:
---------- APA ----------
Cignoli, R. & Torrell, A.T.
(2004)
. Glivenko like theorems in natural expansions of BCK-logic. Mathematical Logic Quarterly, 50(2), 111-125.
http://dx.doi.org/10.1002/malq.200310082---------- CHICAGO ----------
Cignoli, R., Torrell, A.T.
"Glivenko like theorems in natural expansions of BCK-logic"
. Mathematical Logic Quarterly 50, no. 2
(2004) : 111-125.
http://dx.doi.org/10.1002/malq.200310082---------- MLA ----------
Cignoli, R., Torrell, A.T.
"Glivenko like theorems in natural expansions of BCK-logic"
. Mathematical Logic Quarterly, vol. 50, no. 2, 2004, pp. 111-125.
http://dx.doi.org/10.1002/malq.200310082---------- VANCOUVER ----------
Cignoli, R., Torrell, A.T. Glivenko like theorems in natural expansions of BCK-logic. Math. Logic Q. 2004;50(2):111-125.
http://dx.doi.org/10.1002/malq.200310082