No dictionary definitions please, I can get those on my own.
um. here is my general impression then, with no dictionary references.
formal logic is the process(es) by which an argument can be determined as valid or not. An argument is valid if the premises are all true, then the conclusion must also be true.
Importantly, formal logic is only a way to sorting an argument and determining if it is internally consistant, not whether it is actually true (which, more often then not, would require evidence gathered from the outside world).
The word ‘logical’ can also be applied to other processes, and as such can be used almost synonymously with ‘rational’ when applied to people (and Mr. Spock), and ‘deterministic’ when applied to other systems (either natural ones, or engineered ones).
Cheers!
That which tries to avoid the “contradictory item”. The contradictory item however will always win because it can be anything conceivable even not itself. It can be true and false at the same time and at different times, it can be non existent and also exist since it is totally free from any logical constraint. It can be distinguishable and also not. It completely breaks down our thought and language and concepts.
CONTRADICTORY ITEM IS THE ONLY ITEM THAT TRULY EXISTS.
dunno about you nameta, but from my experience the law of non-contradiction works pretty well, ive seen no instance of contradiction ‘winning’ over logic (or even that there was a competition).
a quick note to add, all that can be logically expressed can be done so with the Sheffer Stroke (‘|’ or ‘not and’/NAND or ~[P&Q]), which has the following truth table.
P Q P|Q
T T F
T F T
F T T
F F T
If i remember correctly, early Wittgenstien liked this idea quite a lot.
Unfortunately, it has been discovered that we dont actually use logic by nature, instead we just roughly calculate the possible scenarios and tend to believe what we think is the most likely, sometimes even if it is self-contradictory.
Cheers!
what about “the art/science of right reasoning”? But as stated beforehand, Wittgenstein is a great go-to guy for definition(s) on this stuff. His Tractatus Logico Philosophicus has this kind of stuff sprinkled all through out it. 
This is closest to what I am thinking. Logic is a set of rules to “unpack” the truths in a set of given premises. And the logic of these rules, ie the logic of logic, or meta-logic if you will, as to why they are in themselves true, is that they work or are successful, as derived from empirical observations and as actually experienced.
For example one of this rule is the law of non contradiction which is, if A is true, than (NOT A) is false: something cannot be and not be at the same time. This is a common sensical experience.
Thus logic is not something artificial, ie invented, but merely a discovery of the nature of truths in things as we humanly know it intuitively. The value in the works of people like Aristotle, etc, is to extract and reduce these meta-logic, the set of rules that makes logic, to a small, self-evident, number, such as conjunction (AND), disjunction (OR), negation (NOT), the law of non contradiction, and modus-ponus (the law of implication).
So with just these small set of “thinking tools” we can now go out there into the world to discover all the truths therein. And thus logic is meta-physics, namely that which is necessary to say anything true about “physics”.
Logic is the set of grammatical rules we use to make sure our words are about stuff. I say this because only words are capable of violating logic- premises and things in themselves can’t do it. I don’t see logic at all as the results of observations we’ve made about propositional relationships- that is to say, the laws of logic are not like the laws of physics. We don’t see things out there operating according to these laws, what we see is that if we don’t follow these laws ourselves when communicating, our words lose whatever correspondence they had to the concepts they intend to represent.
Logic gives philosophy “parimeters(sp?)” (for lack of a better word). It keeps philosophical debates from getting irational. If we cannot think at least halfway-rationally, we cannot efective learn anything new from talking philosophy. 
and continuing in the same sentence …
So if seeing is not observation, then arent you losing correspondence with the concepts that you intend to respresent? 