The "logic" behind it is that it is DEFINED that way! You are asking a slightly different question, I think- you want to connect that with out "everyday" idea of "if... then...". And the difficulty with that is our usual concept of "if A then B" does NOT assign a truth value in the case that A is false, no matter what B is. You have to be careful to distinguish between "If A then B" and "A if and only if B". "If A then B" only talks about what happensifA is TRUE. It says nothing at all about what happens if A is false. But for symbolic logic purposes, we must have a value in all cases and it is simplest to assign "true". I like to think of it as "innocent until proven guilty". Suppose a teacher says to his class, "If you get "A" oneverytest, I will give you an "A" in the course." Okay, you get an "A" on every test and get an "A" in the course (the "T->T" case). His statement was obviously true. On the other hand, suppose you get a "B" on every test and get a B for the course (the "F->F" case). Again, his statement is true. But suppose you got an A on every test but one and a B on that one. If he gives you an "A" was his statement false (the F-> T case)? No, because he never said what would happen if you DIDN'T get an A on every test. The only way you could be SURE his statement was false was if you got an A on every test and did NOT get an A in the course (the "T->F" case).