rule of inference

a rule of inference is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).

rules of inference are usually given in the following standard form: $\text{[math]}$

a rule of inference is sound if the conclusion logically follows from the premises

the following isnt a sound rule of inference
$\text{[math]}$ the following is a sound rule of inference
$\text{[math]}$

we arrive from premises to a conclusion with the inference process