谓词逻辑
我正在准备考试，但我不太确定如何描述这一点：
领域就是所有人。
V(w) = w 是选民
P(w) = w 是政治家
K (y, z) = y 知道 z
T (y, z) = y 信任 z
Cal 是一位认识所有人的选民。 （Cal 是 c）
这会是： ∀x V(c)^K(c,x)
存在一个没有其他政治家信任的政治家
∃x∀y P(x)^P(y)^T(y,x) ）
我不确定这些是否正确。最后一个不是说：有些政客没人信任吗？怎样才能让它变得单一呢？
另外：没有人信任每一位政客。
∃x∀y P(y)^T(Øx,y
谢谢
) 我不确定这是否发布在正确的位置，但我认为这将是一个好地方。
I'm studying for an exam, and I'm not really sure how to portray this:
The domain is all people.
V (w) = w is a voter
P (w) = w is a politician
K (y, z) = y knows z
T (y, z) = y trusts z
Cal is a voter who knows everyone.
(Cal is c)
Would this be: ∀x V(c)^K(c,x)
There is a politician that no other politician trusts
∃x∀y P(x)^P(y)^T(y,x)
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?
Also: No one trusts every politician.
∃x∀y P(y)^T(¬x,y)
Thanks
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.
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评论（2）
第一个很好，你是说：
“对于所有人来说，cal 是一个选民，并且 cal 认识那个人”
（顺便说一下，这可以用另一种方式写。你可以将其写为“Cal 是一个选民，并且对于所有人来说 ”人，cal 知道那个人。看起来更自然，更接近原始的简单英语陈述，但它们的意思是相同的）
第二个，你说的是
“存在一个人 x ，对于所有人来说 。人 y, x 是政治家并且 y 是政治家 AND y 信任 x"
试试这个：
∃x∀y:P(x)^(P(y)->(!T(y,x))
（抱歉，我没有使用所有正确的符号D:. -> 表示暗示，而 ! 表示不），这就是说“存在一个人 x，对于所有人 y，x 是一个政治，并且如果 y 是一个政治，则 y 不信任 x”
对于第三个，你想要“对于所有人来说，都存在一个他们不信任的政治家”。
The first one is good, you are saying:
"For all persons, cal is a voter and cal knows that person"
(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)
The second one, you are off. You are saying
"There exists a person x such that for all persons y, x is a politician AND y is a politician AND y trusts x"
Try this:
∃x∀y:P(x)^(P(y)->(!T(y,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"
For the third one, you want to go for "For all persons, there exists a politician that they do not trust".
第一：好
第二：好，但应该是“不是T”吧？
第三：“不是x”意味着什么都没有。你应该用德摩根的说法改写为“对于每个人来说，都有一个他们不喜欢的政客”。
First: good
Second: Good, but it should be "not T", right?
Third: "not x" means nothing. You should use DeMorgan's to rephrase as "For every perspn there is an politician whom they don't like".