Bob has a collection of propositions he believes and a set of inference rules. He'd like to derive more propositions from his existing ones, but this is a computationally intensive process and he's generally forced to just run a naive breadth-first search as a low-priority background task.
Alice has been lucky enough to derive a new proposition recently, using existing propositions that she knows Bob already has. She transmits the complete derivation process to Bob. Bob verifies the derivation process, thus arriving at the new proposition sooner than he would have gotten to it using his own thought processes.
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?