I think it's quite rare that the most important beliefs you should derive from the news can be justified by a collection of absolute statements.

I think you'd be better served by a tool for calculating chains of Bayesian reasoning. I've seen a tool that does this for numerical estimations.

Correct. The only way to not subject oneself to (economic) irrationality is to model your beliefs about the world using probabilities and using Bayes to update in light of new evidence.