"on the justification" is correct and usable in written English.
It is typically used to refer to a justification or explanation for a particular action or decision. For example: "The company decided to terminate the employee for cause, and provided a written explanation of their decision on the justification of the employee's performance."
If one is against abortion on the justification of love for the fetus and human life, how is it possible to hate, yes, hate, women who consider abortion and the doctors who help them.
Blair and Zapatero took opposing views on the justification for military action against Saddam Hussein.
The debate focused on the justification of confronting readers with stark images of an innocent victim of the intensifying refugee crisis.
"I hadn't given it a moment's thought before then, but I wanted to keep him happy so I produced a book on the justification of punishment".
(From "Are you feeling lucky, punk?".) Peter's leader on the justification for the first Gulf war, from January 1991:Benjamin Franklin said there never was a good war, or a bad peace.
Even more important, "In each instance, the Texas Legislature relied on the justification that its discriminatory measures were necessary to combat voter fraud," as it now has with its voter-I.D. law.
The F.B.I. has long used confidential informants — and protected them when they committed crimes — on the justification that criminals in league with other criminals can help catch bigger fish.
While his allies and his enemies have put different spins on the justification for what Mr. Berlusconi said, many of them agree that his comment was unplanned and unproductive.
Sheikh Omar obligingly issued fatwas that allowed attacks on Christians and the plunder of jewelry stores, on the justification that a state of war existed between Christians and Muslims.
One can only imagine the faces in that audience as Mr. Volcker announced, "I'd like to take advantage of your captive presence today, before you scatter into the real world, to reflect a bit on that uniqueness, on the justification for our special role and degree of independence within the government, and on the special responsibilities that independence implies".
The canonists drew together existing Christian traditions on the justification of war and on noncombatant immunity, ideas later developed by various Christian theologians; and the chivalric code contributed further to the idea of noncombatant immunity and also added restraints on the means of war.
