Negation and BCK‐algebras

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Mathematical Logic Quarterly 49 (4):336-346 (2003)
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Abstract

In this paper we consider twelve classical laws of negation and study their relations in the context of BCK‐algebras. A classification of the laws of negation is established and some characterizations are obtained. For example, using the concept of translation we obtain some characterizations of Hilbert algebras and commutative BCK‐algebras with minimum. As a consequence we obtain a theorem relating those algebras to Boolean algebras.

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10.1002/malq.200310035

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Maximal Deductive Systems and Injective Objects in the Category of Hilbert Algebras.Daniel Gluschankof & Miguel Tilli - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (3):213-220.

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