Tautological validity - in all situations, where the premises are true, the conclusion follows.
Were we to get an argument with inconsistent premises, e.g.
P, ¬P ∴ Q
Is tautologically valid
P, ¬ P ⊨ Q
After all, there are no rows where all the premises are true, yet the conclusion is false.
And thus we receive “ex falso sequitur quodlibet”, also known as the principle of explosion. From falsity anything follows.
⊥ ⊨ ⊤
¬ P ∨ ⊥ , P ∨ Q , ⊤ ∴ Q ∧ ⊤
p → q
¬ q → ¬ p
V → E
¬ E → ¬ V