Difference between $\models$ and $\Rightarrow$ What is the difference between $\models$ and $\Rightarrow$ in propositional logic?
 A: In the book "Modeling and reasoning with Bayesian networks", page 14, $\Rightarrow$ is defined to be the material implication connective. Some other authors write this as $\rightarrow$. 
Other authors write $\Rightarrow$ as a synonym for $\models$, which is a connective in the metatheory that indicates logical implication.
Both conventions appear often enough that you have to look at each author's conventions individually.  
A: ⇒ is a logical connective in the object language.  It connects two propositions.  It has a specific truth table and/or a characterization by a set of axioms (or axiom schema) under a rule of inference(s).
$\models$ happens in the metalanguage and usually refers only to semantic entailment.  It doesn't connect individual propositions, but rather relates a proposition or a set of propositions to another proposition or set of propositions.  It doesn't have a truth table.  With $\models$ we can write things likes
$\models$ (p⇒q).
p $\models$ q.
{p, q, r} $\models$ (p⇒(q⇒r)).
There is no meaningful statement like {p, q, r} ⇒ (p⇒(q⇒r)), because ⇒ only relates particular propositions, not sets of propositions.
