Modus Ponens

logic

Definition

Modus Ponens

The modus ponens is a deductive argument form and rule of inference. It can be summarise as

If the antecedent A is true, then the consequent C must also be true.

Formally, for any atoms $A$ and $B$:

$${\frac{A\to BA}{B}}_{(\mathrm{MP})}$$

Soundness

$$KB⊢A\text{implies}KB\models A$$

Completeness

$$KB\models A\text{implies}KB⊢A$$

Frege’s Logic

In Frege’s Logic, modus ponens serves as the fundamental rule of inference that licenses the step from $A\to B$ and $A$ to $B$.