Proof Tableau method: It is a refutation method Does not follow the way humans reason The Deduction property 演绎法 Σ, ϕ |= ψ if and only if Σ |= ϕ → ψ The refutation rule ⊥ Prove ϕ by proving ¬ϕ "¬ϕ" can be interpreted as $ϕ\Rightarrow⊥$ ¬ϕ ... ⊥ $\Rightarrow$ ϕ 横线:假设 竖线:由假设推出的结论 E is modus ponens. I is deduction.