Modus ponens rule:
In fact the general format for the modus ponens rule is as follows: like if we have a true sentence that states the proposition A implies proposition B and we see that proposition A is true, where we can infer that proposition B is true. So the notation we use for this is as follows:
(A→B, A)÷B
Hence it is an example of an inference rule. There is the comma above the line indicates both these things in our knowledge base so we see there the line stands for the deductive step. However, if we know there both the propositions above the line are true so we can deduce in which the proposition below the line is also true. In fact generally, an inference rule as
A ÷B
is sound if we can be sure there that like A entails B, i.e. B is true where A is true. In formally, there A entails B means such as if M is a model of A then M is also a model of B. Than we write this as
After that this gives us a way to check the soundness of propositional inference rules: (i) draw up a logic table for both A and B estimating them for all models, other is (ii) check that where A is true and then B is also true. So here we don't care that about the models for which A is false.