Casus Belli (lat.): A ground for war; an occurrence warranting international hostilities.
~ Brewer, Dictionary of Phrase and Fable.
The threory of
just war stems back to the fourth century, and the writings of St. Augustin. St. Augustin of Hippo wrestled the old anti-violence thoughts of Christianity (as seen by e.g. Jesus) and comes to the conclusion that there are occations where violence is acceptable and even needed.
The thoughts of St. Augustin were later distilled by theologists and canonic lawyers to reach an essence of three criteria to be fulfilled before a war could be justified:
1. Just cause
2. Authority of the prince
3. Right intention
The first two were summed up by Isidore of Sevilla:
That war is lawful and just which is waged upon command in order to recover property or to repel attack. The last criterion ment that the warriors should fight with pure motives, and only as a last practicable mean of achieving the justifiable purpose. Even then no more force than necessary should be used. In addition, violence was considered to be neutral, not 'evil' as today. Since violence itself was neutral it drew moral coloring from its intentions - fighting with good intentions was "good violence".
So - how do we transfer this to CK?
- The dynastic claim is mentioned - if a scoundrel have cheated you or your kin of their rightful inheritance you have a just cause. If you have no higher instances to appeal to you may authorise war (as the prince) as long as other means fail. You have a CB.

- War on heretics were common, depending on the standing Papal definition of a "heretic"

An example is the Albigensian crusade, where the papal legates tried with peaceful means first (thus fulfilling one of the criterias above when they failed) in protection of faith (a just cause).
- War on the heathens and infidel muslims come in the same category. Out of Christian love the best thing you could do was to forve them away from their ungodly ways to save their souls...