Semantic entailment

ϕ₁, …, ϕn ⊨ Ψ

A formula Ψ is semantically entailed by premises (ϕ₁, …, ϕn) if every valuation that makes premises true makes Ψ true.

counterexample makes premises true but not conclusion

if ϕ ⊨ Ψ and Ψ ⊨ ϕ, ϕ ≡ Ψ