A decision or argument based on sound reasoned argument which can be proved - logical.

Disputing an argument on the basis of reasoning means criticizing or challenging the logic and rationale behind the argument rather than attacking the person making the argument. It involves examining the premises and conclusions to determine if they are logically sound and valid.

Both explain the basis for an argument.

A basis is something upon which something is based - a starting point, base or foundation, such as for an argument.

To dispute an argument on the basis of fact means to challenge the validity of the argument by presenting evidence or data that contradicts the claims being made. This approach focuses on objective information rather than relying solely on opinions or personal beliefs. By using facts as a basis for disputing an argument, one aims to strengthen their position and demonstrate the flaws in the opposing point of view.