# 实质条件

• $A \to B$
• $A \supset B$
• $A \Rightarrow B$

## 真值表

$~A$ $~B$ $A \rightarrow B$（符合了「如果A為真，那麼B必為真」）
F F T
F T T
T F F
T T T

## 形式性質

• 如果$\Gamma\models\psi$$\emptyset\models\phi_1\land\dots\land\phi_n\rightarrow\psi$對于某些$\phi_1,\dots,\phi_n\in\Gamma$。（這是演繹定理的特定形式。）
• 上述的逆命題
• $\rightarrow$$\models$而二者都是單調的；就是說如果$\Gamma\models\psi$$\Delta\cup\Gamma\models\psi$，并且如果$\phi\rightarrow\psi$$(\phi\land\alpha)\rightarrow\psi$對於任何α, Δ。（用結構規則的術語說，這叫做弱化。）

• 分配律$A \rightarrow (B \rightarrow C) \rightarrow ((A \rightarrow B) \rightarrow (A \rightarrow C))$
• 傳遞律：($A \rightarrow B) \rightarrow ((B \rightarrow C) \rightarrow (A \rightarrow C))$
• 冪等律$A \rightarrow A$
• 真理保持:在其下所有變量被指派為真值‘真’的釋義生成真值‘真’作為實質蘊涵的結果。
• 交換律：($A \rightarrow (B \rightarrow C)) \equiv (B \rightarrow (A \rightarrow C))$

A → B

B → A

## 引用

• Brown, Frank Markham（2003）, Boolean Reasoning: The Logic of Boolean Equations, 1st edition, Kluwer Academic Publishers, Norwell, MA. 2nd edition, Dover Publications, Mineola, NY, 2003.
• Edgington, Dorothy (2001), "Conditionals", in Lou Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell.
• Edgington, Dorothy (2006), "Conditionals", in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Eprint.
• Quine, W.V.（1982）, Methods of Logic, (1st ed. 1950), (2nd ed. 1959), (3rd ed. 1972), 4th edition, Harvard University Press, Cambridge, MA.