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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.


Documento: Artículo
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
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
Página de inicio:111
Página de fin:125
Título revista:Mathematical Logic Quarterly
Título revista abreviado:Math. Logic Q.


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---------- APA ----------
Cignoli, R. & Torrell, A.T. (2004) . Glivenko like theorems in natural expansions of BCK-logic. Mathematical Logic Quarterly, 50(2), 111-125.
---------- CHICAGO ----------
Cignoli, R., Torrell, A.T. "Glivenko like theorems in natural expansions of BCK-logic" . Mathematical Logic Quarterly 50, no. 2 (2004) : 111-125.
---------- 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.
---------- VANCOUVER ----------
Cignoli, R., Torrell, A.T. Glivenko like theorems in natural expansions of BCK-logic. Math. Logic Q. 2004;50(2):111-125.