P暗示Q,英语怎么读

发布于 2024-08-29 19:03:09 字数 343 浏览 7 评论 0原文

如何理解经典逻辑中P蕴含Q?

示例:

Distributivity:  

Ka(X->Y) -> (KaX -> KaY)

这是使用经典逻辑规则的模态逻辑。
KaX:a 知道 X 为真。

我很好奇英语中的含义怎么读?如果那么别的呢?

编辑:在模态逻辑中,Ka变成Box,它是盒状形状符号,象征着必然规则,规则N,这意味着,盒子P,如果你在世界Delta中有P,那么所有可访问的世界也应该有P。

还有钻石P,这意味着存在一种可能性,即存在一个世界可以从钻石P拥有的世界访问到P。

how to read P implies Q in classical logic?

example :

Distributivity:  

Ka(X->Y) -> (KaX -> KaY)

This is modal logic which uses classical logic rules.
KaX : a knows the that X is true.

I m curious about how to read implication in english? if then else?

Edit : in Modal Logic, Ka becomes Box, well it s boxed shape sign, that symbolizes necessiation rule, Rule N, that means, box P , if you have P in a world Delta then all the acessible worlds should also have P.

THere is also Diamond P, which means possibility, that there exists one world which has P accessible from the world that Diamond P has.

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评论(9

乖乖兔^ω^ 2024-09-05 19:03:09

如果你想象一个现实世界中的小例子,也许会帮助你理解:

火意味着热

这意味着如果有火,就一定有热。如果没有火,由于其他影响(例如阳光明媚:)),可能会产生热量,但也可能没有热量。

如果有火但没有热量,那就有问题了。那么这句话的含义就是错误的。

Perhaps it helps you to understand that if you imagine a small example from the real world:

Fire implies Heat

That means if you have fire, there must be heat. If there is no fire, there can be heat, due to other effects (e.g. sun is shining :) ), but there could as well be no heat.

If you have fire but no heat, somethings wrong. The implication is false then.

空袭的梦i 2024-09-05 19:03:09

“P 蕴含 Q”相当于“如果 P,则 Q”。

"P implies Q" is equivalent to "if P, then Q".

孤蝉 2024-09-05 19:03:09

不是 P 或 Q。你想要这个版本吗?

Not P Or Q. This version you want?

平安喜乐 2024-09-05 19:03:09

翻译一下你的例子:

Distributivity

Ka[Z] : ‘A knows Z is true’

Ka[(X->Y)] -> (Ka[X] -> Ka[Y])

如果A知道从X得出Y,那么从A知道X为真,就可以得出A知道Y为真。

Translating your example:

Distributivity

Ka[Z] : ‘A knows Z is true’

Ka[(X->Y)] -> (Ka[X] -> Ka[Y])

If A knows that from X follows Y, then from A knowing that X is true it follows that A knows that Y is true.

路弥 2024-09-05 19:03:09

P 意味着 Q。你面前有英语。

P implies Q. You have the English in front of you.

︶ ̄淡然 2024-09-05 19:03:09

对我来说,P => Q 最好理解为P 为假,或者 Q 为真

To me, P => Q is best read as P is false, or Q is true

浸婚纱 2024-09-05 19:03:09

如果 P 和 Q 为真,或者 P 为假,则 P 意味着 Q 为真。

如果 P 为真且 Q 为假,则为假。

*编辑:基本上,Svisstack 所说的。

P implies Q is true if P and Q are true, or if P is false.

It is false if P is true and Q is false.

*edit: Basically, what Svisstack said.

橘虞初梦 2024-09-05 19:03:09

有时,如果使用共模态(给定模态的德摩根对偶性),这些分配律和模态逻辑的其他公理会更容易理解。那么必然性的共模性就是必然性。对于 a 知道 P 意味着 a 不知道 P:直观上这意味着 a的知识与P并不矛盾,因此a可以在不知道矛盾的情况下学习P。如果a知道P,就说Ca P

那么使用经典逻辑,分配性就相当于:

Ka(X or Y) -> (KaX or CaY)

这种形式通常比形式操作中带有蕴涵的形式更容易处理。

Sometimes these distributivity laws, and other axioms of modal logic, are easier to grasp if you use the comodalities, which are the De Morgan dualities of given modalities. The comodality of necessity is then necessity. For a to coknow P means that a does not know not P: intuitively it means that a's knowledge does not contradict P, so a could learn P without coming to know a contradiction. Say Ca P if a coknows P.

Then using classical logic, distributivity is equivalent to:

Ka(X or Y) -> (KaX or CaY)

This form is often easier to handle that the form with implication in formal manipulations.

人心善变 2024-09-05 19:03:09

您是否正在寻找 P -> 的定义关于如何在写作或说话时实际用文字表达它的问题或建议?如果是前者,已经有一些好的建议了。

但是,如果是后者,我建议简单地说“P 意味着 Q”,正如您在帖子中已经使用的那样。它很简洁,除非您与对数理逻辑不太熟悉或不熟悉的人交谈,否则它的含义是明确的。

Are you looking for a definition of the P -> Q or advice on how to actually say this express it in words when writing or speaking? If it's the former, there are already some good suggestions.

However, if the latter, I would suggest simply saying "P implies Q" as you've already used in your post. It's succinct, and unless your talking to someone with limited or no familiarity with mathematical logic, it's meaning is clear.

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