Negation and BCK‐algebras

descriptionPublicationkeyboard_double_arrow_right Article 13 May 2003 English Publisher:WileyJournal:Mathematical Logic Quarterly, volume 49, pages 336-346 (issn: 0942-5616, eissn: 1521-3870,

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Authors: Francisco Miguel García-Olmedo; Antonio J. Rodríguez Salas;

doi: 10.1002/malq.200310035

Negation and BCK‐algebras

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Abstract

AbstractIn 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.

Related Organizations

University of Granada
Spain

Keywords

BCK-algebras, BCI-algebras, BCK-algebras with negation, negation in algebraic structures, Other algebras related to logic, Hilbert algebras

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