Glivenko like theorems in natural expansions of BCK-logic
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...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_09425616_v50_n2_p111_Cignoli |
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| Sumario: | 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. |
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