# 实质条件

（重定向自逻辑条件

• ${\displaystyle A\to B}$
• ${\displaystyle A\supset B}$
• ${\displaystyle A\Rightarrow B}$

## 真值表

${\displaystyle ~A}$  ${\displaystyle ~B}$  ${\displaystyle ~A\rightarrow ~B}$ （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${\displaystyle \Gamma \models \psi }$ ${\displaystyle \emptyset \models \phi _{1}\land \dots \land \phi _{n}\rightarrow \psi }$ 對于某些${\displaystyle \phi _{1},\dots ,\phi _{n}\in \Gamma }$ 。（這是演繹定理的特定形式。）
• 上述的逆命題
• ${\displaystyle \rightarrow }$ ${\displaystyle \models }$ 而二者都是單調的；就是說如果${\displaystyle \Gamma \models \psi }$ ${\displaystyle \Delta \cup \Gamma \models \psi }$ ，并且如果${\displaystyle \phi \rightarrow \psi }$ ${\displaystyle (\phi \land \alpha )\rightarrow \psi }$ 對於任何α, Δ。（用結構規則的術語說，這叫做弱化。）

• 分配律${\displaystyle A\rightarrow (B\rightarrow C)\rightarrow ((A\rightarrow B)\rightarrow (A\rightarrow C))}$
• 傳遞律：(${\displaystyle A\rightarrow B)\rightarrow ((B\rightarrow C)\rightarrow (A\rightarrow C))}$
• 冪等律${\displaystyle A\rightarrow A}$
• 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：(${\displaystyle A\rightarrow (B\rightarrow C))\equiv (B\rightarrow (A\rightarrow C))}$

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.
• Quine, W.V.（1982）, Methods of Logic, (1st ed. 1950), (2nd ed. 1959), (3rd ed. 1972), 4th edition, Harvard University Press, Cambridge, MA.