So you're rephrasing the concept of argumentation in terms of computational complexity and crypto. Interesting! Definitely something worth thinking about. I would only suggest that you link your use of "SAT" with Boolean Satisfiability problem so people don't confuse it with the aptitude test.

All I can add right now is that you maybe shouldn't exclude the "trusted arguer" case you mention here:

If Bob trusts Alice though, Bob could be persuaded by simply recieving a claim from Alice.

Intuitively, being informed that the relevant expert has reached a conclusion should suffice to move your probability distribution, and instances of doing this are typically classified as arguments, e.g. "Mainstream physicists hold that ... so you should too.". (Though perhaps for your purposes here there's a reason to exclude it?)

Formally, Alice may persuade Bob of an assertion by presenting a signature for the claim, generated from the private key of the expert, where the signature is verifiable from the expert's public key in polynomial time. (In everyday use, of course, Alice doesn't need to involve a public key infrastructure; she would just show Bob a trusted, hard-to-modify book or hyperlink to a hard-to-hack, known website that speaks for the expert.)