For faster navigation, this Iframe is preloading the Wikiwand page for 吸收律.

吸收律

维基百科,自由的百科全书

抽象代数中,吸收律是连接一对二元运算恒等式

任何两个二元运算比如 $ 和 %,服从吸收律如果:

a $ (a % b) = a % (a $ b) = a.

运算 $ 和 % 被称为对偶对。

设有某个集合闭合在两个二元运算下。如果这些运算是交换律结合律的,并满足吸收律,结果的抽象代数就是,在这种情况下这两个运算有时叫做。因为交换律和结合律经常是其他代数结构的性质,吸收律是的定义性质。由于布尔代数Heyting代数是格,它们也服从吸收律。

因为经典逻辑布尔代数的模型,直觉逻辑Heyting代数的模型,吸收律对分别指示逻辑或逻辑与的运算

吸收律的证明

  

(P ∨ 0) ∧ (P ∨ Q) = P ∨ (0 ∧ Q) = P ∨ 0 = P

(P ∧ 1) ∨ (P ∧ Q) = P ∧ (1 ∨ Q) = P ∧ 1 = P

这里的 = 号要理解为公式上的逻辑等价

吸收律对相干逻辑线性逻辑亚结构逻辑不成立。在亚结构逻辑情况下,在恒等式的定义对的自由变量之间没有一一对应

{{bottomLinkPreText}} {{bottomLinkText}}
吸收律
Listen to this article

This browser is not supported by Wikiwand :(
Wikiwand requires a browser with modern capabilities in order to provide you with the best reading experience.
Please download and use one of the following browsers:

This article was just edited, click to reload
This article has been deleted on Wikipedia (Why?)

Back to homepage

Please click Add in the dialog above
Please click Allow in the top-left corner,
then click Install Now in the dialog
Please click Open in the download dialog,
then click Install
Please click the "Downloads" icon in the Safari toolbar, open the first download in the list,
then click Install
{{::$root.activation.text}}

Install Wikiwand

Install on Chrome Install on Firefox
Don't forget to rate us

Tell your friends about Wikiwand!

Gmail Facebook Twitter Link

Enjoying Wikiwand?

Tell your friends and spread the love:
Share on Gmail Share on Facebook Share on Twitter Share on Buffer

Our magic isn't perfect

You can help our automatic cover photo selection by reporting an unsuitable photo.

This photo is visually disturbing This photo is not a good choice

Thank you for helping!


Your input will affect cover photo selection, along with input from other users.