What does $\Leftrightarrow$ Mean?

Asked Jul 11 '22 at 14:42

Active Jul 11 '22 at 14:42

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I know that in set theory the notation $\Leftrightarrow$ usually means “if and only if” however recently I’ve seen lots of modal logic statements written I such a way that they use the symbols $\Leftrightarrow$ and $\equiv$ synonymously. So can someone please explain what does $\Leftrightarrow$ mean in modal logic.

asked Jul 11 '22 at 14:42

2

$$A \iff B$$ is exactly equivalent to the compound statement $$(A \implies B) ~~~\text{and}~~~ (B \implies A).$$ – user2661923 Jul 11 '22 at 14:45
Here and here is a perspective (well, mine). – ryang Jul 11 '22 at 15:21
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You need to cite a specific text that is causing you a problem. There is no general agreement about the usage of these symbols and nothing specific to modal logic AFAIK. – Rob Arthan Jul 11 '22 at 20:16

What does $\Leftrightarrow$ Mean?

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