基本邏輯名詞

2009/02/25
~ 阿亮 ~

最近看到一些簡單的邏輯 (Logic) 英詞名詞,並不是很清楚,所以,找出來再複習一下。

其實大部份是很簡單的,只是換成英文就不熟了.

Rules of Inference

 Modus Ponens

\displaystyle\begin{array}{l}
p\rightarrow q \\
p \\
\therefore q
\end{array}

 

 Modus Tollens

\begin{array}{l}
p\rightarrow q \\
\neg q \\
\therefore \,\neg p
\end{array}

 

 Hypothetical Syllogism

\begin{array}{l}
p\rightarrow q \\
q\rightarrow r \\
\therefore p\rightarrow r
\end{array}

 

 Disjunctive Syllogism

\begin{array}{l}
p\vee q \\
\neg p \\
\therefore q
\end{array}

 Constructive Dilemma

\begin{array}{l}
(p\rightarrow q) \wedge (r\rightarrow s) \\
p\vee r \\
\therefore q\vee s
\end{array}

 

 Absorption

\begin{array}{l}
\,\\
p\rightarrow q \\
\therefore p\rightarrow (p\wedge q)
\end{array}

 Simplification

\begin{array}{l}
\\
p\wedge q \\
\therefore p
\end{array}

 

 Conjunction

\begin{array}{l}
p \\
q \\
\therefore p\wedge q
\end{array}

 

 Addition

\begin{array}{l}
\\
p \\
\therefore p \vee q
\end{array}

 

 

Rules of Replacement

Double Negation p\leftrightarrow \,\neg\neg p
Commutation \begin{array}{l} \\  (p\vee q)\leftrightarrow  (q\vee p) \\ (p\wedge q)\leftrightarrow  (q\wedge p) \\ \end{array}
Tautology \begin{array}{l} \\  p\leftrightarrow  (p\vee p) \\ p\leftrightarrow  (p\wedge p) \\ \end{array}
Association

\begin{array}{l} \\ \left[p\vee  (q\vee r)\right] \leftrightarrow  \left[(p\vee  q)\vee r\right] \\  \left[p\wedge  (q\wedge r)\right] \leftrightarrow  \left[(p\wedge  q)\wedge r\right] \\ \end{array}

Transposition \begin{array}{l} \\  (p\rightarrow q) \leftrightarrow  (\neg q\rightarrow \neg p) \\ \end{array}
Material Implication \begin{array}{l} \\  (p\rightarrow q) \leftrightarrow  (\neg p\vee q) \\ \end{array}
Exportation  \begin{array}{l} \\  \left[(p\wedge q)\rightarrow r }\right]  \leftrightarrow   \left[p\rightarrow (q\rightarrow r)\right]   \\ \end{array}
Material Equivalence

\begin{array}{l} \\
(p\leftrightarrow q)\leftrightarrow \left[(p\rightarrow q) \wedge (q\rightarrow p)\right] \\
 (p\leftrightarrow q)\leftrightarrow \left[(p\wedge q) \vee (\neg p \,\wedge \neg q)\right] \\
\end{array}

Distribution

\begin{array}{l} \\
\left[p \wedge (q\vee r)\left] \leftrightarrow \left[(p\wedge q)\vee (p\wedge r)\right] \\
\left[p \vee (q\wedge r)\left] \leftrightarrow \left[(p\vee q)\wedge (p\vee r)\right] \\
\end{array}

De Morgan’s Theorems

\begin{array}{l} \\
\neg(p \wedge q)\leftrightarrow (\neg p \,\vee \neg q) \\
\neg(p \vee q)\leftrightarrow (\neg p \,\wedge \neg q) \\
\end{array}

 

 

Bi-conditionals Logical Equivalence

(\forall x)(\psi x\rightarrow \varphi x) \leftrightarrow  \,\neg(\exists x)(\psi x \,\wedge \neg\varphi x)

"Everything in the lake is wet." 

is logically equivalent to

"There isn’t anything in the lake which is not wet."

 

(\exists x)(\psi x\wedge \varphi x) \leftrightarrow  \,\neg(\forall x)(\psi x \rightarrow \,\neg\varphi x)

"There exists at least one individual who is both a native of Boston and of Irish descent."

is logically equivalent to

"It’s not true that no natives of Boston are of Irish descent."

 

(\forall x)(\psi x\rightarrow \neg\varphi x) \leftrightarrow \,\neg(\exists x)(\psi x \wedge \varphi x)

"No residents of Boston are Irish."

is logically equivalent to

"It’s not true that some residents of Boston are Irish."

 

(\exists x)(\psi x \,\wedge \neg\varphi x) \leftrightarrow \,\neg(\forall x)(\psi x \rightarrow \varphi x)

 "Some residents of Boston are not Irish."

is logically equivalent to

"Not all residents of Boston are Irish."

 

 

 



站內搜尋



本站其他服務

本站其他軟體



  • 下一台單車(NextBike)

    打開定位即搜尋附近二十點自行車站點,不塞滿全部站點資料到整個地圖上,所以畫面簡潔方便看清楚目前所在地,若需要搜尋地圖其他位置附近站點,再點擊地圖即可。


  • 下一班高鐵 (nextTHSR)

    這個 app 只要開啟後,就根據定位幫你過濾出最近高鐵站的時刻表,不用再按任何按鈕了,方便您在很快時間內確定要坐的哪一班高鐵


  • 條碼掃描器(QRCode)

    支援 QRCode and Barcodes、可連續快速掃描、自動對焦、可打開手電筒供掃描時使用


  • 照片去背(PhotoEraser)

    一款方便移除背景的工具,產生透明背景圖可以存回原本相簿,也可分享到其他 App 使用.


  • 姓名筆畫吉凶查詢系統

    這是一個提供中文字康熙筆畫的小軟體,並根據農民曆計算每個名字或公司名的總筆畫以及最後的吉凶數,共有四種模式


  • 藝文快訊

    讓你可以輕鬆追蹤含有您想要關注關鍵詞的任何藝文活動訊息,只要有最新的資訊,「藝文快訊」即會推播通知給你.