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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