I'm not familiar with this symbol, how to parse it?

Question

In the context of propositional logic I've encountered this $|=$ symbol that I'm not familiar with. What does it mean? Does it behave like an implication?

Here's where I found it.

https://en.wikipedia.org/wiki/List_of_logic_symbols last line in table — randomgirl, Mar 01 '16 at 06:57
It's called a double turnstile: https://en.wikipedia.org/wiki/Double_turnstile — Christopher Carl Heckman, Mar 01 '16 at 06:58
I think a collection of these constitute the perfect answer. Thanks! — Morgan Wilde, Mar 01 '16 at 07:00
BTW you can type it as $\models$ $\models$ or $\vDash$. $\vDash$ . — Martin Sleziak, Mar 01 '16 at 07:54

score 1 · Accepted Answer · answered Mar 01 '16 at 07:03

If $\varphi$ and $\psi$ are sentences of propositional logic, $\varphi\vDash\psi$ means that the sentence $\varphi\to\psi$ is true under any assignment of truth values to the propositional variables occurring in $\varphi$ and $\psi$. In your question there are no propositional variables to which truth values can be assigned, so the question is in effect asking which of the following sentences are true:

$\text{False}\to\text{True}$
$\text{True}\to\text{False}$

I'm not familiar with this symbol, how to parse it?

1 Answers1