The coolest thing is that it would actually make a distilled "skeleton of beliefs" that supported each perspective. You could quickly understand alternate points of view by skimming the assertion graph. It would encourage critical thinking about one's own perspective as well. You could even do belief "theory-crafting" by toggling beliefs on or off and seeing what the logical consequences would be for different claims credibility.
Instead of disagreements turning into character attacks it could be a very discrete "you agree with assertion [url to assertion and evidence/counter-evidence] and I do not."