Time travel is of course rife with the potential to cause all sorts of causality paradoxes. One solution is that what is in the past has happened, and nothing you can do can change it in any way. Under this assumption, if you travel back in time to kill your grandfather before he sires your father, then no matter how you attempt to achieve it, you fail - simply because history tells you that he did sire your father.

This is actually one of the most workable methods of resolving time travel paradoxes in science fiction and in roleplaying gaming. Obviously you exist... so obviously your grandfather must have lived to sire your father.

Or did he?

If the only evidence you have is the word of your grandmother, then maybe she was lying about who your grandfather really was. So if you go back and kill the guy who she says is your grandfather, you might be able to do it after all. Without causing a paradox, because he wasn't really your grandfather...

In this form of time travel, research and irrefutable proof of events in the past become important. Anything that has been recorded is likely to have really happened. Unless the recording was faked by time travellers...

You see, this form of rigid and inflexible past is quite interesting in terms of developing a time travel story. Probably moreso than a world in which you can change the past - and where you don't have to worry about making things consistent.