谓词逻辑 [英] Predicate Logic

问题描述

我正在为考试而学习，我不太确定如何描述这个问题:

I'm studying for an exam, and I'm not really sure how to portray this:

领域就是所有人.

V(w)= w是选民
P(w)= w是政客
K(y，z)= y知道z
T(y，z)= y信任z

V (w) = w is a voter
P (w) = w is a politician
K (y, z) = y knows z
T (y, z) = y trusts z

卡尔是一个认识所有人的选民. (Cal是c)

Cal is a voter who knows everyone. (Cal is c)

会是:∀xV(c)^ K(c，x)

Would this be: ∀x V(c)^K(c,x)

有一个政客没有其他政客信任

There is a politician that no other politician trusts

∃x∀yP(x)^ P(y)^ T(y，x)

∃x∀y P(x)^P(y)^T(y,x)

我不确定那些说法是否正确.最后一个人不会说:有没有人信任的政治家吗?如何使其单数化?

I'm not sure if those are right. Wouldn't the last one be saying: There are politicians that no one trusts? How do I make it singular?

也:没有人相信每一个政客.

Also: No one trusts every politician.

∃x∀yP(y)^ T(¬x，y)

∃x∀y P(y)^T(¬x,y)

谢谢

P.S.我不确定这是否发布在正确的位置，但我认为这是个好地方.

P.S. I'm not sure if this is posted in the right place, but I assume this would be a good place for it.

推荐答案

第一个很好，你在说:

对于所有人而言，cal都是选民，cal知道该人"

"For all persons, cal is a voter and cal knows that person"

(顺便说一句，这可以用另一种方式写.您可以这样写:卡尔是选民，对所有人来说，卡尔都知道那个人.这看起来会更自然一些，更接近原始的纯英语声明，但它们是同一回事)

(This could be written another way, by the way. You could write it as "Cal is a voter and for all persons, cal knows that person. Would seem a bit more natural and closer to the original plain english statement, but they mean the same thing)

第二个，您离开了.你在说

The second one, you are off. You are saying

存在一个人x，因此对于所有人y，x是政治人物，而y是政治人物，并且y信任x"

"There exists a person x such that for all persons y, x is a politician AND y is a politician AND y trusts x"

尝试一下:

∃x∀y:P(x)^(P(y)->(！T(y，x))

∃x∀y:P(x)^(P(y)->(!T(y,x))

(对不起，我没有使用所有适当的符号D :.->表示暗含，！表示不是)，所以这是说存在一个人x，对于所有人y，x都是政治人物并且，如果y是策略，则y不信任x"

(Sorry, I didn't use all of the proper symbols D:. -> means implies, and ! means not) so this is saying "There exists a person x such that for all persons y, x is a politicion AND if y is a polition, y does not trust x"

对于第三个人，您想参加对于所有人，都有一个他们不信任的政治家".

For the third one, you want to go for "For all persons, there exists a politician that they do not trust".

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