. There are different kinds of logic (one is very science-based, the other isn't). Neither form of logic is really an "art". That is, logic isn't about expressing emotions. Furthermore, both forms of logic have consistent rules. Logic is about successfully applying these rules.
There are two kinds of logic: inductive logic and deductive logic.
The first kind, inductive logic, is what we use when making any scientific argument . Inductive logic takes our observations about the world and uses them to come to conclusions about things that we can't yet directly observe. Basically, scientific inquiry is just a combination of observing the world and applying inductive logic. Here's a classic example of an inductive argument:
All crows I have seen have been black.
I have seen a large percentage of all the crows that exist.
Therefore, all crows are probably black.
Deductive logic deals with what must be true. Most (it can get a bit more complicated than this) deductive logic deals with claims that apply to an entire class of things. For example, if I know that all (the entire class) bachelors are men, and I know that Jim is a bachelor, it is necessarily true that Jim is a man. Because ALL members of the class (bachelors) are men, it holds that every particular instance of the class must be a man.
Deductive logic isn't really science or art. Unlike science, deductive logic doesn't really have much to do with empirical observations. Art is more about expressing emotions. That's not what deductive logic is about. You can understand deductive logic as a way of defining things that helps us to clarify our reasoning.
If you'd like to know more about deductive and inductive logic (as well as their differences) please let me know and I can post a hub about it.