In this case, contradiction isn't worrisome due to explosion, because the paper uses an intuitionistic logic that doesn't explode. It's a different question - if we have evidence for A and also evidence against A, what should we believe regarding A?
Paraconsistent logics might help with that, of course.
When I was working on the model of argumentation referred to above, Tony Hunter and Philippe Besnard started to look at paraconsistent logics. But these typically end up supporting conclusions that are somewhat counter intuitive. So they moved towards the preferred solution in the argumentation community of working with consistent subsets as the basis for an argument. In the case where we have on un-attacked argument for A and another against A then it is hard (not possible?) to find a rational way of preferring one or other outcome. Most models of argumen...
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?