So IIUC like if an article is covering a debate, 3 sources assert "A", and another 3 assert "~A", then the heuristic "3 sources assert means it's true", gives you a logical setup with "A ^ ~A"?

If so, then yes that's a bug in that heuristic. Like I said in my first comment, what OP is describing is impossible the way they're describing it. So I think in that sense we're in agreement.

But on the other hand, maybe OP will end up hacking together a thing that resembles probabilistic modal logic.

At the time I wrote that comment OP was being downvoted and there were no encouraging responses, which I felt wasn't representative of the math community as I know it. Now there is a good discussion of the problem space and some suggestions to check out different kinds of logic, so I'm glad to see all that going on!