As for the axioms of modal logic - perhaps they don't apply, but modal logic was developed specifically to handle assertions of possibility and impossibility, necessity and contingency. Anyway, you guys are the ones asserting that a logical contradiction exists between determinism and free will. I am the one denying that such a contradiction exists. If you guys are right, there is some valid proof of "if determinism is true, there's no free will." If I'm right, there is no such proof. It's unreasonable to demand that I go through every conceivable proof-attempt and refute it - the burden should be on you guys to construct the proof. Use any logic system you want (if it's esoteric, like I guess modal logic may be, it should come with some explanation of why it applies.)
OK, I'll give it a shot. Be careful with the phrase "there can be more than one future". That almost sounds like many-worlds interpretation of QM, where multiple futures all actually happen.
What determinism says is that for any two times, the laws of nature posit a definitive 1:1 mapping between states of the universe at those times. If the state of the universe at time 1 is A, then the state at time 2 is X; if B, then Y; if C, then Z, etc. It can't happen that one half of one of these pairs happens without the other. But, since there is no necessity about A or B or C, there is no necessity about X or Y or Z. And vice versa: since there is no necessity about X or Y or Z, there is no necessity about A, B, C.
Notice that I didn't specify which time is earlier, and which is later. On most deterministic theories that have been seriously proposed for physics, determinism is bi-directional. Later events plus laws of nature entail a specification of earlier events, just as much as the other way around. This raises the interesting question: if you're not worried about the correspondence between future events and the choice you're making right now, why worry about the correspondence with past events? Suppose someone 100 years from now writes, "On Feb 12 2007, warpus did X", and this sentence is true. That doesn't conflict with your free will - does it? So why would it conflict with your free will that, in principle, someone with an awful lot of knowledge 100 years ago could have written that sentence?