Some doubts about the differences between logic implication and inference rule I am studying for an Artificial Inteligence university exam that includes a section dedicated to mathematical logic.  I am finding some difficulty in understanding the difference between logical implication and inference rules in logic.
For example I can write
All men are mortal AND Socrates is a man → Socrates is mortal
and I think that this is a classic logic implication because I can verify that it is true that All men are mortal and, at the same time, I can verify that is true that Socrates is a man, so then I can say that Socrates is a mortal because if the left side of implication is true then it is so is right side.
And, at this point I have my first doubt related to the fact that, looking at the truth table for logical implication I found that:
$A \to B$ is TRUE if $A$ is TRUE and $B$ is TRUE, but also that
$A \to B$ is TRUE if $A$ is FALSE and $B$ is TRUE and
$A \to B$ is TRUE if $A$ if FALSE and $B$ is FALSE.
Then reading on Wikipedia I find this:

In logic, a rule of inference, inference rule, or transformation rule
  is the act of drawing a conclusion based on the form of premises
  interpreted as a function which takes premises.

And moreover (from the Italian version of Wikipedia):

The inference is the process by which a proposition accepted as true,
  it moves to a second proposition whose truth is derived from the
  contents of the first.

So I am beginning to think that my original vision of logical implication was not totally correct because when I use the logic implication in this way:
$A \to B$ I have to know the boolean value of $A$ and of $B$ and then I evaluate the logical value of the implication $A \to B$, but this process says nothing about the value of $B$ having a previous knowledge of the value of $A$.
So is it correct say that “affirm something about $B$ using a previous knowledge about $A$,” is an inference rule?
Can you give me some clarification about it and about the previous example regarding: “Socrates is a man, all men are mortal, therefore Socrates is mortal”?

I think you confuse syntax with semantics. Modus ponens is syntactical notion whether your analysis of mortal Socrate is semantical.
