Seine Argumentation war völlig unlogisch und schwer nachvollziehbar.

His argumentation was completely illogical and difficult to follow.

Deine Argumentation ist völlig unlogisch und widerspricht den Fakten.

Your reasoning is completely illogical and contradicts the facts.

Es wäre unlogisch, das Experiment jetzt abzubrechen.

It would be illogical to stop the experiment now.