Implicative data analysis is a specific method of data analysis, employing asymmetrical similarities and based on the construction of an ascendant binary hierarchical classification. This construction leads to a binary oriented tree. Our contribution is devoted to the analysis of the formal aspects of two versions of the binary tree obtained by an ascendant hierarchical classification: symmetrical and assymmetrical. New axiomatization is proposed for both of them. More precisely, the passage between the formal definitions of a binary symmetrical tree and a binary oriented one, is studied accurately.