Glivenko like theorems in natural expansions of BCK‐logic

Mathematical Logic Quarterly 50 (2):111-125 (2004)
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Abstract

The classical Glivenko theorem asserts that a propositional 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

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References found in this work

An algebraic approach to intuitionistic connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
On The Role of The Polynomial →Y in Some Implicative Algebras.Antoni Torrens - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (2):117-122.

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