1. Survival is the primary goal of all civilizations.
Agree.
2. Resources in the universe are finite.
True in the theoretical sense, but false in the practical sense.
3. Civilizations cannot be certain of others’ intentions.
Not obviously true or false.
4. Communication is dangerous.
This is such a strong axiom and is almost certainly false.
Its conclusion from applying the four axioms is that preemptive annihilation is the rational strategy.
As an alien civilization, if your strategy for survival in the cosmos is to "immediately and totally annihilate any sign of life", then that is almost a surely losing strategy. If intelligent life is prevalent, and the cost of annihilating a species is so low that they can just do it willy-nilly, then all it takes is one surviving colony to use the same superweapon against you and you're finished. Oh, you'd also have to be annihilating species left and right across the galaxy without revealing your location. And in the worst case, you've just pissed off all the known alien entities in your galactic neighborhood. Good luck to you.
It makes for fun writing, but I don't understand how anyone can take it seriously.
> Not obviously true or false.
"Intentions are uncertain" is true, though.
If you are claiming that it is possible to be certain of other civilisations intentions, I am very skeptical.