1)The most common academical definition is a study of arguments. Such a study is mostly concerned with deductive reasoning. E.G separating arguments that are valid from invalid. A valid argument is known as one where the conclusion is entailed by the premise, an invalid is one where a conclusion can be false whilst the premises are true.
2)Some academical definitions expand onto inductive. This has little to do with deductive validity or invalidity, it has more to do with how likely arguments are to be true. Under this very broad definition of logic, it is simply defined as a method that determines how likely an argument is to arrive at the truth. An argument that is deemed very likely to do so is called inductively strong and one that is not likely is regarded as inductively weak.
3)Conventional people tend to regard logic as simply any chain of reasoning. A logician's reasoning contains just as much 'logic' as that of a politician or a Jerry Springer attendant. In addition to this, they tend to regard whatever they think is good, true or in a way desirable as 'logical'. In short, they tend to see it as a mere rhetorical instrument to make a certain viewpoint worthy of reflection or acceptance.
4)In conclusion, it may be possible to arrive at a clear and a consistent academical definition of logic, especially if we embrace the definition of point 1 and discard the definition of point 2, yet when dealing with ordinary people, we are far less likely to. That is the case simply because they tend to regard anything that they think is agreeable to their own views as 'logic' or 'logical'.
