I am doing propositional logic at the minute but I have come across a symbol I have never seen before and its meaning is not explained in my lecture notes. Here is an image of what I am talking about. Thanks for your help.
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Your image isn't loading, but I'm guessing you mean $\vDash$? – Clive Newstead Jul 21 '17 at 12:08
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take a look here – Masacroso Jul 21 '17 at 12:08
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Well the $\models$ wikipedia page helped you ? – Furrane Jul 21 '17 at 12:11
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@cliveNewstead thats the one! Could you give me an example of it in use that I can use as reference for future questions? – Jordan Jul 21 '17 at 12:14
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The "double turnstile" $\vDash$ is "\vDash" enclosed between dollar signs. – Mauro ALLEGRANZA Jul 21 '17 at 12:18
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The image is:
$$\models $$
In logic, this means that the RH side is the logical consequence of the LH side. That is, in every possible model the RH side is true given that every element in the LH side is satisfied by the model. If the LH side is a model instead of a set of axioms, it means the RH side is true in the model.
An example probably helps illustrate what is going on. Say we have
$$p_0,p_1 \in\Phi $$
Now, in every possible model where both of those propositions are satisfied, one of them is also satisfied so we can say:
$$\Phi \models p_1$$
On the other hand if we have a model $\mathfrak A$, which has as its domain {1}, then we can say:
$$\mathfrak A \models 1=1$$
(Assuming the rules of usual predicate calculus).
Dole
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