Geodesic
Implication algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 2, pp. 141-153

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We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence properties.
Keywords: implication algebra, pre-implication algebra, orthoimplication algebra, orthosemilattice, congruence kernel 
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Chajda, Ivan. Implication algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 2, pp. 141-153. http://geodesic.mathdoc.fr/item/DMGAA_2006_26_2_a0/