@rschwieb My question seems to be opinion based and lacks clarity. For example , I forgot to mention "practicality" and "conceptual correctness" in my question , which is quite an unpleasant error. So if a MSE users recommendation doesn't satisfy my needs , then it is largly MY fault. Maybe I should delete it and ask a better one next time...
I guess I have to be a Logician to be competent enough to ask this kind of question because there are so many technicalities.