That is a nice paper, thanks. I particularly liked the idea of "epistemic entrenchment ordering" - if and when we encounter the enemy (contradiction), what will we sacrifice first?
I didn't entirely understand the section on adding disjunction; it was quite brief, and it seemed like somone had an insight, or at least, encountered a stumbling block and then found a workaround.
Ideally, I think you'd like to allow "arguing in the alternative", where if you can derive the same conclusion from several individually consistent (though mutually inconsistent) scenarios, the support for the conclusion should be stronger than it could be committing to any one scenario.
But that doesn't seem to be possible?
if and when we encounter the enemy (contradiction), what will we sacrifice first?
See also the notion of http://en.wikipedia.org/wiki/Paraconsistent_logic .
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?