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.)
Background on Agorics:
The idea of software agents cooperating in an open market or "agora". Described by Mark Miller and Eric Drexler here: http://e-drexler.com/d/09/00/AgoricsPapers/agoricpapers.html Depicted by Greg Egan in his novel "Diaspora", exerpt here: http://gregegan.customer.netspace.net.au/DIASPORA/01/Orphanogenesis.html
Background on Argument: http://en.wikipedia.org/wiki/Argument
Let's start by supposing that an argument is a variety of persuasive message. If Bob trusts Alice though, Bob could be persuaded by simply recieving a claim from Alice. That is a kind of persuasive message, but it's not an argument. If Bob is insecure, then Bob's mind could be hacked and therefore changed. However, that's not an argument either. (The "Buffer Overflow Fallacy"?)
Possibly arguments are witnesses (or "certificates"), as used in computational complexity. Alice could spend exp-time to solve an instance of an NP-complete problem, then send a small witness to B, who can then spend poly-time to verify it. The witness would be an argument.
I'm not sure if that's a definition, but we have an overgeneral category (persuasive messages) that is, a superset of arguments, two subcategories of persuasive messages that are specifically excluded, and one subcategory that is specifically included, which seems like enough to go on with.
We know what witnesses to SAT problems look like - they look like satisfying assignments. That is, if Bob were considering a SAT problem, and Alice sent Bob a putative satisfying assignment, and Bob verified it, then Bob ought (rationally) to be convinced that the problem is satisfiable.
What do other kinds of witnesses look like? What about probabilistic computation? What if Alice and Bob may have different priors?