Entailment vs Inference

KB entails alpha means that if the KB is true then so must alpha.

KB |- alpha  (i.e. alpha can be infered from KB) just means that
with some inference procedure we can derive alpha. The difference
between entailment and inference is that inference procedures 
cannot necessarily find everything that can be entailed and
inference procedures are not necessarily correct/sound (i.e. can
derive things that aren't necessarily true). 

For example, the abduction rule states:

P => Q, Q        cavities cause toothaches, I have a toothache
---------        -------------------------------------------
P                therefore I have a cavity

This is an example of unsound inference. Although this type of reasoning
can be useful, P is not necessarily true (i.e. the KB does not
entail P) -- there could be another cause of the toothache.

The example with Phd's and salary earnings at the end of the lecture
notes on FOL is an example where Modus Ponens cannot find everything
that is entailed by the KB (i.e. Modus Ponens cannot infer rich(ME),
but resolution can).