Logic and truth values

[robvalue]

I've been very interested in logic recently, but it's not a subject I have studied much. I did a bit of basic Boolean algebra, and I've read that there are a lot of different logic systems that can be used.

I started from the idea that a particular statement can have a truth value of 0 (false) or 1 (true).

(a) Is a sentence by default true or false? In computer programming (what I've done anyway), it is the case that any statement is true until it includes a false element. The point I'm getting at is what would be the truth value of an empty statement? One that says nothing at all. I would assume it would be true.

(b) What about a statement that is nonsense? One that makes no sense, either at all, or in the syntax of accepted statements. Would it be treated as actually saying nothing, so would revert to (a)? Or is it just not allowed?

I find also the idea of paradoxical statements interesting, generally ones that reference themselves in some way. For example, "this statement is false." I have read that there are several ways of approaching this problem, I think my favourite is to add in the implication that if a statement is being made, it is asserting that it is true in what it is saying. So it becomes, "This statement is true. This statement is false." And then it can be seen to be false.

The problem with the liar paradox is that the opposite of false is true. But I wonder if you could define truth value to be 1 if it is consistent, and 0 otherwise. So the liar paradox cannot have truth value 1, since this does not check out. So it has value 0. I may have not thought that through properly though.

If anyone has any links to websites which address these kinds of thing particularly well (I already checked out wikipedia hehe) then feel free! Thanks