I am looking for ways to crowd-source systematic reasoning behind common and uncommon convictions, beliefs, science principles, software or product design, political views, etc. Today, discussions on such topics happen in both formal & informal media, like newspapers, blogs, emails, scientific literature, e-groups, etc. Such discussions use the tools, style and expressions of natural language and are also hugely diverse in presentation.
The disadvantage of this type of discourse is that the rigor behind a certain claim cannot always be evaluated easily. It's fairly complex to figure all the missing pieces, unstated assumptions, specious logic, etc.
The best case would be a system that can auto-derive conclusions, figure out contradictions, incompleteness, unsoundness, etc. but that's probably too far at this point. For a start am looking for a simple system that would allow me to represent Boolean statements like: "z is true iff (x OR y) is true", etc., along with axioms that one declares true. The statement themselves could just be in a natural language form.
Such a system would help in rigorously representing scientific answers like for "Why is the sky blue?", convictions like "Why should I homeschool my child?", "Why is the US dollar not a good bet in the long run?", "Why is climate change caused by human activity?", "Why does C++ have to do this?", etc.
As you'd see many of the above questions come with too many points & counter points to be rigorously represented in regular forums. In most cases it's just different axioms that drive disagreeing parties away from each other. Calling out axioms explicitly simplifies the evaluation of an argument.
The system am looking for would be able to present a claim with finality like: "Given the following axioms/assumptions, the statement .... is true.". It would also be able to represent the chain of reasoning as appropriate.
A simple vision for such a system is to represent short statements (restricting perhaps to a tweet-like length of 144 chars), their truth-value condition (as a Boolean expression) and the axioms to start out with.
Do we have such systems/websites available? Thoughts?