Persona 3 & 4 only share samekind of battle system, persona fusion and name. Other than that they are different games. Just like Final fantasy games there are no sequels or prequels. You don't need to know nothing about p4 except that its really good game.
It shouldn't be a problem if you haven't played any of the games in the series. The storyline is not connected to the other games although you will see some cameos from the other games but it wont be a problem.
The strong shall live, the weak shall perish. Survival of the fittest. - Shishio Makoto