Note that I have removed the factorization requirement from the definition of a language in Fundamental Knowledge Part 1; so we will just have This will remove some triviality in examples of fuzzy logic systems in the upcoming post. The original motivation behind the factorization was that traditionally compound terms are considered formulas, but terms themselves are not considered formulas. I don’t really see why we can’t let terms be formulas; let us assume “substitutions” have already been made.
I have also removed the requirement that for all in a theory where is a logic system. Instead I have defined a logic system that satisfies this condition as a normal logic system.