From professional experience (I've been a programmer since the 80's and was paid for it from the 90's onward) I agree with you entirely re. graphical representation. That doesn't keep generation after generation of tool vendors crowing that thanks to their new insight, programming will finally be made easy thanks to "visual this, that or the other". UML being the latest such to have a significant impact.

You have me pondering what we might gain from whipping up a Domain-Specific Language (say, in a DSL-friendly base language such as Ruby) to represent arguments in. It couldn't be too hard to bake some basics of Bayesian inference into that.