语义蕴涵关系意味着什么(M | = A)？

Question

我读过很多关于它的文章.他们将其描述为:

在逻辑中,意义通常由满足关系描述

M | = A.

描述情况M何时满足公式A.

所以,我也搜索了一些例子.我找到了以下示例:

True | = False = false

False | = True = true

我根本不明白.在这些情况下它意味着什么？

Answer 1

(假设你谈论命题逻辑(它类似于其他逻辑,如pred.逻辑))

对于两个公式A和B:

A |= B 
"B evaluates to true under all evaluations that evaluate A to true"

对于一组公式M和公式B:

M |= B
"for every evaluation: B evaluates to true if only all elements of M
 evaluate to true"

来你的例子:

true |= false 
is incorrect since evaluations exist


false |= A
is correct for any formula A, since 'false' is never evaluated to 'true'
under any evaluation

rgrds.