There is a dramatic use of this in Robert Forward's novel Timemaster.
There is a backwards-in-time wormhole in space, and the good guy manages
to maneuver things so that the bad guy gets destroyed. One space ship
comes out of the wormhole before it goes in, bounces off another one,
and knocks its earlier self in, or something like that.
I still say that it is black magic. Once you start up one of these
Novikov collisions, you won't be able to interfere. The whole path is
pre-ordained. Any universes where you succeed get nulled out.
Remember Asimov's short story about the crystals which dissolve *before*
you add water? The military used them to create a bomb by using a cascade
of stages to expand the time interval. Once a crystal dissolved there
*had* to be ("had been") water added in a few hours. Drop the bomb in a
heavily sealed case in an enemy country, and a bizarre, damaging typhoon
would arise sufficient to bash open the bomb, along with everything else.
Not contradictory or inconsistent, but paradoxical in my book.
Hal